A229113 Row sums of triangle A166890.

1, 3, 14, 115, 1474, 26306, 605538, 17116241, 574398861, 22333212354, 987660842174, 48969675370286, 2690888441513773, 162333780684342177, 10667116965172284025, 758434434866124781819, 58015602766701416940599, 4750972163883049286678765, 414721061026426313701858479

Offset

0,2

Comments

Triangle A166890 transforms diagonals in the table of coefficients of successive iterations of x*(1+x)^2 (cf. A166888).

Links

Table of n, a(n) for n=0..18.

Example

Triangle A166890 begins:
1;
2, 1;
9, 4, 1;
78, 30, 6, 1;
1038, 364, 63, 8, 1;
18968, 6233, 986, 108, 10, 1;
443595, 139008, 20685, 2072, 165, 12, 1;
12681960, 3833052, 545736, 51494, 3750, 234, 14, 1; ...
of which the row sums form this sequence.

Prog

(PARI) {a(n, k)=local(F=x, M, N, P, m=max(n, k), A166890); M=matrix(m+2, m+2, r, c, F=x; for(i=1, r+c-2, F=subst(F, x, x+2*x^2+x^3+x*O(x^(m+2)))); polcoeff(F, c)); N=matrix(m+1, m+1, r, c, M[r, c]); P=matrix(m+1, m+1, r, c, M[r+1, c]); A166890=P~*(N~)^-1; sum(k=0, n, A166890[n+1, k+1])}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A166890.

Sequence in context: A265001 A279429 A333797 * A180435 A256159 A122081

Adjacent sequences: A229110 A229111 A229112 * A229114 A229115 A229116

Keyword

nonn

Author

Paul D. Hanna, Sep 13 2013

Status

approved