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%I #6 Oct 06 2013 14:42:33
%S 1,1,2,34,773,36656,3001377,333647780,58561139773,13838291852092,
%T 4280413527001849,1779704699369214238,931039792575220097699,
%U 604786686422678514970170,489307443863919174036440087,478922652139578822529676247092,560120417434857039499787289137249
%N G.f.: Sum_{n>=0} x^n / (1-x)^(n^5).
%F a(n) = Sum_{k=0..n} binomial(k^5 + n-k-1, n-k).
%e G.f.: A(x) = 1 + x + 2*x^2 + 34*x^3 + 773*x^4 + 36656*x^5 + 3001377*x^6 +...
%e where
%e A(x) = 1 + x/(1-x) + x^2/(1-x)^32 + x^3/(1-x)^243 + x^4/(1-x)^1024 + x^5/(1-x)^3125 + x^6/(1-x)^7776 +...
%o (PARI) {a(n)=polcoeff(sum(k=0,n,x^k/(1-x+x*O(x^n))^(k^5)),n)}
%o for(n=0,20,print1(a(n),", "))
%o (PARI) {a(n)=sum(k=0,n,binomial(k^5+n-k-1, n-k))}
%o for(n=0,20,print1(a(n),", "))
%Y Cf. A178325, A230050, A227934.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Oct 06 2013
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