A211892 - OEIS

%I #7 Nov 06 2013 23:14:33

%S 1,3,12,198,16962,6762210,11473594848,80455865485692,

%T 2306084412391039038,268657100633050977422322,

%U 126765866001055606588876061400,241678197713843578271875740922972788,1858396158245858742065123341776166504084452

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

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

%e G.f.: A(x) = 1 + 3*x + 12*x^2 + 198*x^3 + 16962*x^4 + 6762210*x^5 +...

%e such that

%e 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 +...

%e Jacobsthal numbers begin:

%e A001045 = [1,1,3,5,11,21,43,85,171,341,683,1365,2731,5461,10923,21845,...].

%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^2)*x^k/k)+x*O(x^n)), n)}

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

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

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

%K nonn

%O 0,2

%A _Paul D. Hanna_, Apr 24 2012