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

0,2

Links

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

Formula

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

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

Crossrefs

Cf. A104980, A104988.

Sequence in context: A184818 A352370 A007808 * A119906 A059726 A274379

Adjacent sequences: A104986 A104987 A104988 * A104990 A104991 A104992

Keyword

nonn

Author

Paul D. Hanna, Apr 10 2005

Status

approved