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A104989
Row sums of triangle A104988, which equals the matrix square of triangle A104980.
3
1, 3, 13, 69, 433, 3133, 25657, 234537, 2367825, 26176981, 314670353, 4088360569, 57112939433, 853922061413, 13609089281849, 230346936181465, 4127180489763649, 78046835384582069, 1553536327234953153
OFFSET
0,2
LINKS
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
Sequence in context: A184818 A352370 A007808 * A119906 A059726 A274379
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 10 2005
STATUS
approved