A211893 G.f.: exp( Sum_{n>=1} 3 * Jacobsthal(n)^n * x^n/n ), where Jacobsthal(n) = A001045(n).

1, 3, 6, 36, 561, 98211, 43176384, 116622937722, 1022189210900601, 41675008108242048327, 6377839090284322052067558, 4114890941608928235401688095580, 10460015732506081308723488849683574907, 108482611110966450613465001912856742180485969

Offset

0,2

Comments

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

Links

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

Formula

G.f.: exp( Sum_{n>=1} (2^n - (-1)^n)^n / 3^(n-1) * x^n/n ).

Example

G.f.: A(x) = 1 + 3*x + 6*x^2 + 36*x^3 + 561*x^4 + 98211*x^5 + 43176384*x^6 +...
such that
log(A(x))/3 = x + x^2/2 + 3^3*x^3/3 + 5^4*x^4/4 + 11^5*x^5/5 + 21^6*x^6/6 + 43^7*x^7/7 +...+ Jacobsthal(n)^n*x^n/n +...
Jacobsthal numbers begin:
A001045 = [1,1,3,5,11,21,43,85,171,341,683,1365,2731,5461,10923,...].

Prog

(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)^k*x^k/k)+x*O(x^n)), n)}
for(n=0, 16, print1(a(n), ", "))

Crossrefs

Cf. A211892, A211894, A211895, A211896, A207971, A207972, A001045.

Cf. A231292 (Jacobsthal(n)^n).

Sequence in context: A264702 A077532 A174666 * A093800 A068776 A355544

Adjacent sequences: A211890 A211891 A211892 * A211894 A211895 A211896

Keyword

nonn

Author

Paul D. Hanna, Apr 24 2012

Status

approved