A216352 G.f.: A(x) = exp( Sum_{n>=1} A000172(n)^2*x^n/n ) where Franel number A000172(n) = Sum_{k=0..n} C(n,k)^3.

1, 4, 58, 1256, 35771, 1200188, 45016678, 1827941560, 78753548245, 3551810922324, 166120394053698, 8002733850225288, 395089619067741926, 19911864121386482264, 1021345223473335336668, 53190166903606336969840, 2807000233813092463820488, 149869216802426305919295328

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Example

 G.f.: A(x) = 1 + 4*x + 58*x^2 + 1256*x^3 + 35771*x^4 + 1200188*x^5 +...
such that
log(A(x)) = 4*x + 100*x^2/2 + 3136*x^3/3 + 119716*x^4/4 + 5071504*x^5/5 +...+ A000172(n)^2*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)^2*x^m*1^m/m+x*O(x^n)))); polcoeff(A, n)}
for(n=0, 31, print1(a(n), ", "))

Crossrefs

Cf. A166990, A216353, A216354, A216355, A052144, A000172.

Sequence in context: A240430 A334991 A216795 * A295406 A229528 A109056

Adjacent sequences: A216349 A216350 A216351 * A216353 A216354 A216355

Keyword

nonn

Author

Paul D. Hanna, Sep 04 2012

Status

approved