A177449 G.f.: Sum_{n>=0} a(n)*x^n/(1+x)^(3*n^2) = 1+x.

1, 1, 3, 30, 586, 17865, 756285, 41440056, 2805638310, 227131872654, 21459076173105, 2322336372705030, 283667666439112350, 38643426990067599005, 5813534115429573742587, 957883907138024944675200

Offset

0,3

Links

Table of n, a(n) for n=0..15.

Formula

a(n) = number of subpartitions of the partition [0,2,10,24,44,...,3(n-1)^2-(n-1)] for n>0 with a(0)=1. See A115728 for the definition of subpartitions.

Example

1+x = 1 + 1*x/(1+x)^3 + 3*x^2/(1+x)^12 + 30*x^3/(1+x)^27 + 586*x^4/(1+x)^48 + 17865*x^5/(1+x)^75 + 756285*x^6/(1+x)^108 +...

Prog

(PARI) {a(n)=local(F=1/(1+x+x*O(x^n))); polcoeff(1+x-sum(k=0, n-1, a(k)*x^k*F^(3*k^2)), n)}

Crossrefs

Cf. A177447, A177448, A177450.

Sequence in context: A365653 A301663 A319940 * A184900 A274797 A092677

Adjacent sequences: A177446 A177447 A177448 * A177450 A177451 A177452

Keyword

nonn

Author

Paul D. Hanna, May 09 2010

Status

approved