A227935 G.f.: Sum_{n>=0} x^n / (1-x)^(n^5).

1, 1, 2, 34, 773, 36656, 3001377, 333647780, 58561139773, 13838291852092, 4280413527001849, 1779704699369214238, 931039792575220097699, 604786686422678514970170, 489307443863919174036440087, 478922652139578822529676247092, 560120417434857039499787289137249

Offset: 0

Author

Paul D. Hanna, Oct 06 2013

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + 2*x^2 + 34*x^3 + 773*x^4 + 36656*x^5 + 3001377*x^6 +...
where
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 +...
		

Crossrefs

Cf. A178325, A230050, A227934.

Programs

PARI

{a(n)=polcoeff(sum(k=0,n,x^k/(1-x+x*O(x^n))^(k^5)),n)}
for(n=0,20,print1(a(n),", "))

PARI

{a(n)=sum(k=0,n,binomial(k^5+n-k-1, n-k))}
for(n=0,20,print1(a(n),", "))

Formula

a(n) = Sum_{k=0..n} binomial(k^5 + n-k-1, n-k).