A186240 G.f. A(x) defined by A(x) = 1 +x*A(x) +x^2*A(x)^2 +3*x^3*A(x)^3.

1, 1, 2, 7, 21, 66, 228, 799, 2843, 10357, 38278, 143012, 539980, 2056848, 7892496, 30483351, 118416903, 462348219, 1813410078, 7141608015, 28229040165, 111956307486, 445374729396, 1776704142348, 7105896093588, 28487216564476, 114454156300136, 460781265916312

Offset

0,3

Links

Table of n, a(n) for n=0..27.

Vladimir Kruchinin, D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013.

Formula

a(n) = 1/n*sum(j=0..n, binomial(n,j)*sum(i=j..n+j-1, binomial(j,i-j)*binomial(n-j,3*j-n-i-1)*3^(3*j-n-i-1))), n>0

Conjecture: 6*(2*n+3)*(n+1)*a(n) +(277*n^2-191*n-162)*a(n-1) +6*(-155*n^2+305*n-126)*a(n-2) -4*(181*n-195)*(n-2)*a(n-3) -5304*(n-2)*(n-3)*a(n-4)=0. - R. J. Mathar, Sep 27 2013

Mathematica

m = maxExponent = 20;
A[_] = 0; Do[A[x_] = 1 + x A[x] + x^2 A[x]^2 + 3 x^3 A[x]^3 + O[x]^m, {m}];
CoefficientList[A[x], x] (* Jean-François Alcover, Aug 08 2018 *)

Crossrefs

Sequence in context: A052911 A126133 A344500 * A274203 A330058 A220726

Adjacent sequences: A186237 A186238 A186239 * A186241 A186242 A186243

Keyword

nonn

Author

Vladimir Kruchinin, Feb 15 2011

Extensions

Typo in definition corrected by R. J. Mathar, Sep 27 2013

Status

approved