A262008 G.f.: exp( Sum_{n>=1} x^n/n * Sum_{d|n} 2^(d^2) * n^2/d^2 ).

1, 2, 14, 202, 16858, 6746346, 11466918526, 80444425726274, 2306004013900856642, 268654794950929597256002, 126765597355485476411443388062, 241678070949320865028012988979962410, 1858395916568294857820278937430319959202010, 57560683587057503330693629888859064500206488317834

Offset

0,2

Comments

a(n) == 2 (mod 4) for n>0.

Links

Table of n, a(n) for n=0..13.

Example

G.f.: A(x) = 1 + 2*x + 14*x^2 + 202*x^3 + 16858*x^4 + 6746346*x^5 +...
The logarithm of the g.f. begins:
log(A(x)) = 2*x + 24*x^2/2 + 530*x^3/3 + 65632*x^4/4 + 33554482*x^5/5 + 68719479000*x^6/6 + 562949953421410*x^7/7 + 18446744073709814144*x^8/8 +...+ A262009(n)*x^n/n +...
where
A262009(n) = Sum_{d|n} 2^(d^2) * n^2/d^2.

Prog

(PARI) {a(n) = polcoeff( exp(sum(m=1, n, x^m/m * sumdiv(m, d, 2^(d^2) * m^2/d^2))+x*O(x^n)), n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A262009 (log).

Sequence in context: A102224 A123543 A279452 * A054652 A122647 A158097

Adjacent sequences: A262005 A262006 A262007 * A262009 A262010 A262011

Keyword

nonn

Author

Paul D. Hanna, Oct 01 2015

Status

approved