A132006 Column 0 and main diagonal (offset) of triangle A132005.

1, 1, 1, 3, 11, 51, 286, 1886, 14309, 122814, 1176694, 12450056, 144181969, 1814053266, 24640186003, 359363840295, 5601100988553, 92910896970409, 1634289749459611, 30384383699244134, 595344239332647506

Offset

0,4

Comments

Row sums of triangle A132005 yield the factorials. Triangle A132005 is defined by: T(n,k) = T(n-1,k-2) + n*T(n-1,k-1) for n>0 and k>1, with T(n,0) = T(n-1,n-1) for n>0 and T(0,0) = 1.

Links

G. C. Greubel, Table of n, a(n) for n = 0..445

Mathematica

T[n_, k_] := T[n, k] = If[k < 0 || n < k, 0, If[n == 0 && k == 0, 1, If[k == 0, T[n - 1, n - 1], n*T[n - 1, k - 1] + T[n - 1, k - 2]]]]; Table[T[n, 0], {n, 0, 30}] (* G. C. Greubel, Dec 15 2017 *)

Prog

(PARI) { T(n, k)=if(k<0 || n<k, 0, if(n==0 && k==0, 1, if(k==0, T(n-1, n-1), n*T(n-1, k-1)+T(n-1, k-2)))) }; for(n=0, 30, print1(T(n, 0), ", ")) \\ G. C. Greubel, Dec 15 2017

Crossrefs

Sequence in context: A346967 A192925 A350354 * A367011 A020043 A357830

Adjacent sequences: A132003 A132004 A132005 * A132007 A132008 A132009

Keyword

nonn

Author

Paul D. Hanna, Aug 07 2007

Status

approved