0,3

O.g.f.: A(x) = 1 + x/(1-2x) + x^2/((1-2x)*(1-6x)) + x^3/((1-2x)*(1-6x)*(1-12x)) + x^4/((1-2x)*(1-6x)*(1-12x)*(1-20x)) + ...

Also generated by iterated binomial transforms in the following way:

[1,3,13,81,669,6955,88505,...] = BINOMIAL^2([1,1,5,31,253,2673,34833,..]);

[1,5,31,253,2673,34833,541879,...] = BINOMIAL^4([1,1,7,57,577,7389,...]);

[1,7,57,577,7389,115983,2151493,...] = BINOMIAL^6([1,1,9,91,1101,16497,...]);

[1,9,91,1101,16497,301669,..] = BINOMIAL^8([1,1,11,133,1873,32061,..]);

[1,11,133,1873,32061,666579,...] = BINOMIAL^10([1,1,13,183,2941,56529,...]);

etc.

(PARI) a(n)=polcoeff(sum(k=0, n, x^k/prod(j=0, k, 1-j*(j+1)*x+x*O(x^n))), n)

Cf. A135920, A124373.

Adjacent sequences: A135918 A135919 A135920 this_sequence A135922 A135923 A135924

Sequence in context: A112935 A074514 A020014 this_sequence A005923 A089461 A000684

nonn

Paul D. Hanna (pauldhanna(AT)juno.com), Dec 06 2007