A245106 a(n) = Sum_{k=0..n} binomial(n,k) * 2^((n-k)^2) * 3^(k^2).

1, 5, 109, 20825, 43283641, 847757178125, 150104882696162149, 239301431405467344190625, 3433687649167507509801752071921, 443426550049486796441016276819404703125, 515377529600543569431994967945053326153797481949

Offset

0,2

Links

Paul D. Hanna, Table of n, a(n) for n = 0..45

Formula

E.g.f.: ( Sum_{n>=0} 2^(n^2)*x^n/n! ) * ( Sum_{n>=0} 3^(n^2)*x^n/n! ).

a(n) ~ 3^(n^2). - Vaclav Kotesovec, Sep 03 2017

Example

E.g.f.: A(x) = 1 + 5*x + 109*x^2/2! + 20825*x^3/3! + 43283641*x^4/4! + 847757178125*x^5/5! +...
where A(x) = B(x)*C(x) with
B(x) = 1 + 2*x + 2^4*x^2/2! + 2^9*x^3/3! + 2^16*x^4/4! + 2^25*x^5/5! +...
C(x) = 1 + 3*x + 3^4*x^2/2! + 3^9*x^3/3! + 3^16*x^4/4! + 3^25*x^5/5! +...

Prog

(PARI) {a(n)=sum(k=0, n, binomial(n, k)*2^((n-k)^2)*3^(k^2))}
for(n=0, 16, print1(a(n), ", "))

Crossrefs

Cf. A197356.

Sequence in context: A296743 A358781 A188457 * A244004 A003465 A177680

Adjacent sequences: A245103 A245104 A245105 * A245107 A245108 A245109

Keyword

nonn

Author

Paul D. Hanna, Jul 12 2014

Status

approved