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

%I

%S 1,1,3,30,586,17865,756285,41440056,2805638310,227131872654,

%T 21459076173105,2322336372705030,283667666439112350,

%U 38643426990067599005,5813534115429573742587,957883907138024944675200

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

%F 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.

%e 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 +...

%o (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)}

%Y Cf. A177447, A177448, A177450.

%K nonn

%O 0,3

%A _Paul D. Hanna_, May 09 2010

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Last modified January 23 11:42 EST 2022. Contains 350512 sequences. (Running on oeis4.)