Formelsammlung Mathematik: Tabellen: Kombinatorik

Formelsammlung Mathematik

BinomialkoeffizientenBearbeiten

 

n\k −2 −1  0  1 2 3 4 5 6 7 8 9 10 11 12
−4 0 0 1 −4 10 −20 35 −56 84 −120 165 −220 286 −364 455
−3 0 0 1 −3 6 −10 15 −21 28 −36 45 −55 66 −78 91
−2 0 0 1 −2 3 −4 5 −6 7 −8 9 −10 11 −12 13
−1 0 0 1 −1 1 −1 1 −1 1 −1 1 −1 1 −1 1
  0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0
  2 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0
  3 0 0 1 3 3 1 0 0 0 0 0 0 0 0 0
  4 0 0 1 4 6 4 1 0 0 0 0 0 0 0 0
  5 0 0 1 5 10 10 5 1 0 0 0 0 0 0 0
  6 0 0 1 6 15 20 15 6 1 0 0 0 0 0 0
  7 0 0 1 7 21 35 35 21 7 1 0 0 0 0 0
  8 0 0 1 8 28 56 70 56 28 8 1 0 0 0 0
  9 0 0 1 9 36 84 126 126 84 36 9 1 0 0 0
10 0 0 1 10 45 120 210 252 210 120 45 10 1 0 0
11 0 0 1 11 55 165 330 462 462 330 165 55 11 1 0
12 0 0 1 12 66 220 495 792 924 792 495 220 66 12 1
13 0 0 1 13 78 286 715 1287 1716 1716 1287 715 286 78 13
14 0 0 1 14 91 364 1001 2002 3003 3432 3003 2002 1001 364 91


Stirling-Zahlen erster ArtBearbeiten

 

n\k −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9
−6 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
−5 15 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
−4 65 10 1 0 0 0 0 0 0 0 0 0 0 0 0 0
−3 90 25 6 1 0 0 0 0 0 0 0 0 0 0 0 0
−2 31 15 7 3 1 0 0 0 0 0 0 0 0 0 0 0
−1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
  1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
  2 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0
  3 0 0 0 0 0 0 0 2 3 1 0 0 0 0 0 0
  4 0 0 0 0 0 0 0 6 11 6 1 0 0 0 0 0
  5 0 0 0 0 0 0 0 24 50 35 10 1 0 0 0 0
  6 0 0 0 0 0 0 0 120 274 225 85 15 1 0 0 0
  7 0 0 0 0 0 0 0 720 1764 1624 735 175 21 1 0 0
  8 0 0 0 0 0 0 0 5040 13068 13132 6769 1960 322 28 1 0
  9 0 0 0 0 0 0 0 40320 109584 118124 67284 22449 4536 546 36 1


Stirling-Zahlen zweiter ArtBearbeiten

 

n\k −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9
−6 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
−5 15 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
−4 85 10 1 0 0 0 0 0 0 0 0 0 0 0 0 0
−3 225 35 6 1 0 0 0 0 0 0 0 0 0 0 0 0
−2 274 50 11 3 1 0 0 0 0 0 0 0 0 0 0 0
−1 120 24 6 2 1 1 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
  1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
  2 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0
  3 0 0 0 0 0 0 0 1 3 1 0 0 0 0 0 0
  4 0 0 0 0 0 0 0 1 7 6 1 0 0 0 0 0
  5 0 0 0 0 0 0 0 1 15 25 10 1 0 0 0 0
  6 0 0 0 0 0 0 0 1 31 90 65 15 1 0 0 0
  7 0 0 0 0 0 0 0 1 63 301 350 140 21 1 0 0
  8 0 0 0 0 0 0 0 1 127 966 1701 1050 266 28 1 0
  9 0 0 0 0 0 0 0 1 255 3025 7770 6951 2646 462 36 1


Berechnung am ComputerBearbeiten

Funktion Maxima GAP
Binomialkoeffizient binomial(n,k) Binomial(n,k)
Stirling-Zahl erster Art abs(stirling1(n,k)) Stirling1(n,k)
Stirling-Zahl zweiter Art stirling2(n,k) Stirling2(n,k)