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

Author

Paul D. Hanna, Sep 13 2013

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

Cf. A166890.

Programs

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), ", "))