A211892 G.f.: exp( Sum_{n>=1} 3 * Jacobsthal(n^2) * x^n/n ), where Jacobsthal(n) = A001045(n).

1, 3, 12, 198, 16962, 6762210, 11473594848, 80455865485692, 2306084412391039038, 268657100633050977422322, 126765866001055606588876061400, 241678197713843578271875740922972788, 1858396158245858742065123341776166504084452

Offset: 0

Author

Paul D. Hanna, Apr 24 2012

Keywords

• nonn

Comments

Given g.f. A(x), note that A(x)^(1/3) is not an integer series.

Examples

			G.f.: A(x) = 1 + 3*x + 12*x^2 + 198*x^3 + 16962*x^4 + 6762210*x^5 +...
such that
log(A(x))/3 = x + 5*x^2/2 + 171*x^3/3 + 21845*x^4/4 + 11184811*x^5/5 + 22906492245*x^6/6 + 187649984473771*x^7/7 +...+ Jacobsthal(n^2)*x^n/n +...
Jacobsthal numbers begin:
A001045 = [1,1,3,5,11,21,43,85,171,341,683,1365,2731,5461,10923,21845,...].
		

Crossrefs

Cf. A211893, A211894, A211895, A211896, A207972, A001045, A155200.

Cf. A231279 (Jacobsthal(n^2)).

Programs

PARI

{Jacobsthal(n)=polcoeff(x/(1-x-2*x^2+x*O(x^n)),n)}
{a(n)=polcoeff(exp(sum(k=1, n, 3*Jacobsthal(k^2)*x^k/k)+x*O(x^n)), n)}
for(n=0, 16, print1(a(n), ", "))

Formula

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

a(n) = A155200(n) + A155200(n-1).