0,3

O.g.f.: A(x) = 1 + x/(1-x) + x^2/((1-x)*(1-3x)) + x^3/((1-x)*(1-3x)*(1-6x)) + x^3/((1-x)*(1-3x)*(1-6x)*(1-10x)) + ...

Also generated by iterated binomial transforms in the following way:

[1,2,6,25,135,909,7417,71698,...] = BINOMIAL([1,1,3,12,64,433,3567,..]);

[1,3,12,64,433,3567,34905,...] = BINOMIAL^2([1,1,4,20,129,1045,...]);

[1,4,20,129,1045,10209,117069,...] = BINOMIAL^3([1,1,5,30,226,2121,...]);

[1,5,30,226,2121,23919,314605,...] = BINOMIAL^4([1,1,6,42,361,3835,...]);

[1,6,42,361,3835,48885,724569,...] = BINOMIAL^5([1,1,7,56,540,6385,...]);

[1,7,56,540,6385,90519,1490457,..] = BINOMIAL^6([1,1,8,72,769,9993,...]);

etc.

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

Sequence in context: A143917 A009326 A001258 this_sequence A010787 A008933 A020010

Adjacent sequences: A124370 A124371 A124372 this_sequence A124374 A124375 A124376

nonn

Paul D. Hanna (pauldhanna(AT)juno.com), Oct 28 2006