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A180350
G.f.: Sum_{n>=0} a(n)*x^n/n!^5 = [ Sum_{n>=0} x^n/n!^5 ]^3.
3
1, 3, 99, 9237, 775971, 83118753, 10657602909, 1463886204147, 215566192274211, 33677584957306713, 5492032622227428849, 928229455634614797447, 161727023896151286167901, 28905146810167510775300463
OFFSET
0,2
LINKS
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 20 2011
STATUS
approved