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A132006
Column 0 and main diagonal (offset) of triangle A132005.
2
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
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 07 2007
STATUS
approved