A229113 - OEIS

%I #6 Aug 16 2024 18:49:51

%S 1,3,14,115,1474,26306,605538,17116241,574398861,22333212354,

%T 987660842174,48969675370286,2690888441513773,162333780684342177,

%U 10667116965172284025,758434434866124781819,58015602766701416940599,4750972163883049286678765,414721061026426313701858479

%N Row sums of triangle A166890.

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

%e Triangle A166890 begins:

%e 1;

%e 2, 1;

%e 9, 4, 1;

%e 78, 30, 6, 1;

%e 1038, 364, 63, 8, 1;

%e 18968, 6233, 986, 108, 10, 1;

%e 443595, 139008, 20685, 2072, 165, 12, 1;

%e 12681960, 3833052, 545736, 51494, 3750, 234, 14, 1; ...

%e of which the row sums form this sequence.

%o (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])}

%o for(n=0, 25, print1(a(n), ", "))

%Y Cf. A166890.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Sep 13 2013