A104989 Row sums of triangle A104988, which equals the matrix square of triangle A104980.

1, 3, 13, 69, 433, 3133, 25657, 234537, 2367825, 26176981, 314670353, 4088360569, 57112939433, 853922061413, 13609089281849, 230346936181465, 4127180489763649, 78046835384582069, 1553536327234953153

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, A104988.

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, 2];
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))))^-2)[n+1,k+1]))}

Formula

a(n) = Sum_{k=0..n} A104988(n, k).