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A116155
Triangle T(n,k) defined by: T(0,0)=1, T(n,k)=0 if k < 0 or k > n, T(n,k) = T(n-1,k-1) + k*T(n-1,k) + Sum_{j>=1} T(n-1,k+j).
1
1, 0, 1, 1, 1, 1, 2, 3, 3, 1, 7, 9, 10, 6, 1, 26, 33, 36, 29, 10, 1, 109, 135, 145, 134, 70, 15, 1, 500, 609, 645, 633, 430, 146, 21, 1, 2485, 2985, 3130, 3142, 2521, 1182, 273, 28, 1, 13262, 15747, 16392, 16561, 14710, 8733, 2849, 470, 36, 1
OFFSET
0,7
FORMULA
Sum_{k=0..n} T(n,k) = T(n+1,1) = A098742(n+2).
EXAMPLE
Triangle begins:
1;
0, 1;
1, 1, 1;
2, 3, 3, 1;
7, 9, 10, 6, 1;
26, 33, 36, 29, 10, 1;
109, 135, 145, 134, 70, 15, 1;
500, 609, 645, 633, 430, 146, 21, 1;
2485, 2985, 3130, 3142, 2521, 1182, 273, 28, 1;
13262, 15747, 16392, 16561, 14710, 8733, 2849, 470, 36, 1;
MATHEMATICA
T[0, 0]:= 1; T[n_, k_]:= If[k<0 || k>n, 0, T[n-1, k-1] + k*T[n-1, k] + Sum[T[n-1, k+j], {j, 1, n-k-1}]]; Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten (* G. C. Greubel, May 10 2019 *)
PROG
(PARI) {T(n, k) = if(k==0 && n==0, 1, if(k<0 || k>n, 0, T(n-1, k-1) + k*T(n-1, k) + sum(j=1, n-k-1, T(n-1, k+j))))}; \\ G. C. Greubel, May 10 2019
CROSSREFS
Sequence in context: A323850 A236937 A323748 * A365991 A144149 A097005
KEYWORD
nonn,tabl
AUTHOR
Philippe Deléham, Apr 15 2007
EXTENSIONS
Term a(47) corrected in data by G. C. Greubel, May 12 2019
STATUS
approved