A211893 - OEIS

%I #9 Nov 06 2013 23:22:08

%S 1,3,6,36,561,98211,43176384,116622937722,1022189210900601,

%T 41675008108242048327,6377839090284322052067558,

%U 4114890941608928235401688095580,10460015732506081308723488849683574907,108482611110966450613465001912856742180485969

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

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

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

%e G.f.: A(x) = 1 + 3*x + 6*x^2 + 36*x^3 + 561*x^4 + 98211*x^5 + 43176384*x^6 +...

%e such that

%e 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 +...

%e Jacobsthal numbers begin:

%e A001045 = [1,1,3,5,11,21,43,85,171,341,683,1365,2731,5461,10923,...].

%o (PARI) {Jacobsthal(n)=polcoeff(x/(1-x-2*x^2+x*O(x^n)),n)}

%o {a(n)=polcoeff(exp(sum(k=1, n, 3*Jacobsthal(k)^k*x^k/k)+x*O(x^n)), n)}

%o for(n=0, 16, print1(a(n), ", "))

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

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

%K nonn

%O 0,2

%A _Paul D. Hanna_, Apr 24 2012