A216356 a(n) = A000172(n^2), where Franel number A000172(n) = Sum_{k=0..n} C(n,k)^3.

1, 2, 346, 5280932, 6332299624282, 548057409594239814752, 3282684865686445066146128050420, 1329153351023643434414727317328867397924832, 35862023917618878200052422822926970148356592776600354650, 63875599229358329592315180101212796802405282289343043273094466311541144

Offset

0,2

Links

Table of n, a(n) for n=0..9.

Formula

Forms the logarithmic derivative of A216355 after ignoring initial term a(0).

Example

 L.g.f.: L(x) = 2*x + 346*x^2/2 + 5280932*x^3/3 + 6332299624282*x^4/4 + 548057409594239814752*x^5/5 +...
where exp(L(x)) = 1 + 2*x + 175*x^2 + 1760658*x^3 + 1583078442003*x^4 + 109611485085305859618*x^5 +...+ A216355(n)*x^n +...

Prog

 (PARI) {a(n)=sum(k=0, n^2, binomial(n^2, k)^3)}
for(n=0, 15, print1(a(n), ", "))

Crossrefs

Cf. A216355, A166990, A216352, A216353, A216354, A000172.

Sequence in context: A248172 A064501 A063831 * A064023 A370483 A179959

Adjacent sequences: A216353 A216354 A216355 * A216357 A216358 A216359

Keyword

nonn

Author

Paul D. Hanna, Sep 04 2012

Status

approved