0,3

O.g.f.: A(x) = 1 + x/(1-x) + x^2/((1-x)*(1-4x)) + x^3/((1-x)*(1-4x)*(1-9x))

+ x^4/((1-x)*(1-4x)*(1-9x)*(1-16x)) + ...

Also generated by iterated binomial transforms in the following way:

[1,2,7,37,264,2433,27913,...] = BINOMIAL([1,1,4,21,151,1422,16629,..]);

[1,4,21,151,1422,16629,234529,...] = BINOMIAL^3([1,1,6,43,393,4596,...]);

[1,6,43,393,4596,66049,1125905,...] = BINOMIAL^5([1,1,8,73,811,11274,...]);

[1,8,73,811,11274,191685,...] = BINOMIAL^7([1,1,10,111,1453,23328,...]);

[1,10,111,1453,23328,456033,...] = BINOMIAL^9([1,1,12,157,2367,43014,...]);

etc.

(PARI) a(n)=polcoeff(sum(k=0, n, x^k/prod(j=0, k, 1-j^2*x+x*O(x^n))), n)

Cf. A135921, A124373.

Sequence in context: A135164 A072597 A125515 this_sequence A001515 A144301 A083659

Adjacent sequences: A135917 A135918 A135919 this_sequence A135921 A135922 A135923

nonn

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