A216353 G.f.: A(x) = exp( Sum_{n>=1} A000172(n)^3*x^n/n ) where Franel number A000172(n) = Sum_{k=0..n} C(n,k)^3.

1, 8, 532, 62624, 10964914, 2399234384, 609215149096, 171739556144192, 52316948995446679, 16918106849112020088, 5736533516906891508780, 2021549577502367744673888, 735516733692051220039803750, 274907827442478316252748869104, 105138174536582510069969443280760

Offset

0,2

Links

Table of n, a(n) for n=0..14.

Example

 G.f.: A(x) = 1 + 8*x + 532*x^2 + 62624*x^3 + 10964914*x^4 + 2399234384*x^5 +...
where
log(A(x)) = 2^3*x + 10^3*x^2/2 + 56^3*x^3/3 + 346^3*x^4/4 + 2252^3*x^5/5 + 15184^3*x^6/6 + 104960^3*x^7/7 +...+ A000172(n)^3*x^n/n +...

Prog

 (PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, sum(j=0, m, binomial(m, j)^3)^3*x^m*1^m/m+x*O(x^n)))); polcoeff(A, n)}
for(n=0, 31, print1(a(n), ", "))

Crossrefs

Cf. A166990, A216352, A216354, A216355, A052144, A000172.

Sequence in context: A272357 A241367 A121740 * A145182 A089671 A112035

Adjacent sequences: A216350 A216351 A216352 * A216354 A216355 A216356

Keyword

nonn

Author

Paul D. Hanna, Sep 04 2012

Status

approved