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%I #5 Oct 06 2013 19:47:51
%S 1,1,2,10,65,564,6191,82050,1295263,23764278,499547080,11892550569,
%T 317112508944,9392408105655,306739296397827,10973970687363844,
%U 427724034697254939,18073023112616933860,824247511186225346295,40415810147764633887442,2123162727678797736474583
%N G.f.: Sum_{n>=0} x^n / (1-x)^(n^3).
%F a(n) = Sum_{k=0..n} binomial(k^3 + n-k-1, n-k).
%F Equals row sums of triangle A230049.
%e G.f.: A(x) = 1 + x + 2*x^2 + 10*x^3 + 65*x^4 + 564*x^5 + 6191*x^6 + 82050*x^7 +...
%e where
%e A(x) = 1 + x/(1-x) + x^2/(1-x)^8 + x^3/(1-x)^27 + x^4/(1-x)^64 + x^5/(1-x)^125 + x^6/(1-x)^216 + x^7/(1-x)^343 +...
%o (PARI) {a(n)=polcoeff(sum(k=0,n,x^k/(1-x+x*O(x^n))^(k^3)),n)}
%o for(n=0,25,print1(a(n),", "))
%o (PARI) {a(n)=sum(k=0,n,binomial(k^3+n-k-1, n-k))}
%o for(n=0,25,print1(a(n),", "))
%Y Cf. A230049, A178325, A227934, A227935.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Oct 06 2013
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