A180350 G.f.: Sum_{n>=0} a(n)*x^n/n!^5 = [ Sum_{n>=0} x^n/n!^5 ]^3.

1, 3, 99, 9237, 775971, 83118753, 10657602909, 1463886204147, 215566192274211, 33677584957306713, 5492032622227428849, 928229455634614797447, 161727023896151286167901, 28905146810167510775300463

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..424

Formula

a(n) = Sum_{k=0..n} C(n,k)^5 * Sum_{j=0..k} C(k,j)^5 = Sum_{k=0..n} C(n,k)^5 * A005261(k).

Example

G.f.: A(x) = 1 + 3*x + 99*x^2/2!^5 + 9237*x^3/3!^5 + 775971*x^4/4!^5 +...
A(x)^(1/3) = 1 + x + x^2/2!^5 + x^3/3!^5 + x^4/4!^5 +...

Prog

(PARI) {a(n)=if(n<0, 0, n!^5*polcoeff(sum(m=0, n, x^m/m!^5+x*O(x^n))^3, n))}
(PARI) {a(n)=sum(k=0, n, binomial(n, k)^5*sum(j=0, k, binomial(k, j)^5))}

Crossrefs

Cf. A002893, A005261, A141057, A172434, A336270.

Sequence in context: A167582 A068420 A276188 * A293952 A303826 A128296

Adjacent sequences: A180347 A180348 A180349 * A180351 A180352 A180353

Keyword

nonn

Author

Paul D. Hanna, Jan 20 2011

Status

approved