A225601 a(n) = A000172(n)^n, where A000172(n) = Sum_{k=0..n} binomial(n,k)^3 forms the Franel numbers.

1, 2, 100, 175616, 14331920656, 57921784155180032, 12255108779062338588246016, 140335244044685299494850396160000000, 89108073653130217591789722357691598453905367296, 3194443255354428321611505213481524389463527731906791539474432

Offset: 0

Author

Paul D. Hanna, Aug 03 2013

Keywords

• nonn

Examples

			L.g.f.: L(x) = 2*x + 100*x^2/2 + 175616*x^3/3 + 14331920656*x^4/4 + 57921784155180032*x^5/5 +...
where exponentiation is an integer series:
exp(L(x)) = 1 + 2*x + 52*x^2 + 58640*x^3 + 3583098592*x^4 + 11584364000042912*x^5 +...+ A216354(n)*x^n +...
		

Crossrefs

cf. A216354, A000172.

Programs

PARI

{a(n)=sum(k=0,n, binomial(n, k)^3)^n}
for(n=0,20,print1(a(n),", "))

Formula

L.g.f.: Sum_{n>=1} a(n)*x^n/n = log( Sum_{n>=0} A216354(n)*x^n ).