A186242 G.f. A(x) given by A(x) = 1+x*A(x)^2+x^2*A(x)^4+2*x^3*A(x)^6.

1, 1, 3, 13, 62, 317, 1707, 9529, 54634, 319838, 1903895, 11488985, 70122538, 432126645, 2685003765, 16802798157, 105811579002, 670008272170, 4263402119458, 27248174904238, 174836857576628, 1125847862614733, 7273384212430489, 47128196689500189

Offset

0,3

Links

Table of n, a(n) for n=0..23.

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

Formula

a(n) = 1/(2*n-1)*sum(j=0..2*n-1, binomial(i=j..n+j-1, 2*n-1,j)*sum(binomial(j,i-j)*binomial(2*n-j-1,3*j-3*n-i+1)*2^(3*j-3*n-i+1))), n>0.

Mathematica

m = maxExponent = 20;
A[_] = 0;
Do[A[x_] = 1 + x A[x]^2 + x^2 A[x]^4 + 2 x^3 A[x]^6 + O[x]^m, {m}];
CoefficientList[A[x], x] (* Jean-François Alcover, Aug 08 2018 *)

Crossrefs

Sequence in context: A141786 A122122 A093424 * A367060 A350478 A276893

Adjacent sequences: A186239 A186240 A186241 * A186243 A186244 A186245

Keyword

nonn

Author

Vladimir Kruchinin, Feb 15 2011

Status

approved