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A132008
Row sums of triangle A132007.
2
1, 3, 14, 98, 954, 12242, 199156, 3988248, 96094356, 2735515916, 90647239704, 3453539346232, 149695821098056, 7316061672718152, 400012182207670288, 24301065118906010048, 1630456684740565109904, 120168318315515773499952
OFFSET
0,2
COMMENTS
Triangle T=A132007 is defined by: T(n,k) = T(n,k-1) + n*T(n-1,k-1) for n>=k>0, with T(n,0) = T(n-1,n-1) for n>0 and T(0,0) = 1; also, column 0 (A110083) obeys: T(n+1,0) = Sum_{k=0..n} (n!/k!)*C(n,k)*T(k,0).
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], T[n, k - 1] + n*T[n - 1, k - 1]]]]; Table[Sum[T[n, k], {k, 0, n}], {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), T(n, k-1)+n*T(n-1, k-1)))) }; for(n=0, 20, print1(sum(k=0, n, T(n, k)), ", ")) \\ G. C. Greubel, Dec 15 2017
CROSSREFS
Sequence in context: A074515 A336947 A038051 * A140963 A284759 A284760
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 07 2007
STATUS
approved