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

Author

Paul D. Hanna, Apr 10 2005

Keywords

• nonn

Links

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

Crossrefs

Cf. A104980, A104990.

Programs

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 *)

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]))}

Formula

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