A104991 Row sums of triangle A104990, which equals the matrix cube of triangle A104980.

1, 4, 22, 142, 1048, 8704, 80386, 817786, 9093340, 109794556, 1431360958, 20047830262, 300343272952, 4793871035416, 81232799446906, 1456671526257106, 27562347560513524, 548844246683051860, 11474015910364016086

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..440

Formula

a(n) = Sum_{k=0..n} A104990(n, k).

Mathematica

nmax:=30;
T[n_, k_]:= T[n, k] = If[k<0 || k>n, 0, If[k==n, 1, If[k==n-1, n, k*T[n, k+1] + Sum[T[j, 0]*T[n, j+k+1], {j, 0, n-k-1}]]]]; (* T=A104980 *)
M:= M= With[{q = nmax}, Table[If[j>i, 0, T[i, j]], {i, 0, q}, {j, 0, q}]];
f:= f= MatrixPower[M, 3];
a[n_]:= a[n]= Sum[f[[n+1, k+1]], {k, 0, n}];
Table[a[n], {n, 0, nmax}] (* G. C. Greubel, Jun 08 2021 *)

Prog

(PARI) {a(n)=if(n<0, 0, sum(k=0, n, (matrix(n+1, n+1, m, j, if(m==j, 1, if(m==j+1, -m+1, -polcoeff((1-1/sum(i=0, m, i!*x^i))/x+O(x^m), m-j-1))))^-3)[n+1, k+1]))}

Crossrefs

Cf. A104980, A104990.

Sequence in context: A369504 A243626 A369485 * A368562 A027391 A134988

Adjacent sequences: A104988 A104989 A104990 * A104992 A104993 A104994

Keyword

nonn

Author

Paul D. Hanna, Apr 10 2005

Status

approved