cp's OEIS Frontend

A258656 O.g.f.: exp( Sum_{n>=1} A256357(n^2)*x^n/n ), where exp( Sum_{n>=1} A256357(n)*x^n/n ) = 1 + Sum_{n>=1} x^(n^2) + x^(2*n^2).

%I A258656 #10 Jun 16 2015 22:10:39
%S A258656 1,1,3,5,2,10,13,23,43,57,66,96,183,229,375,509,619,883,1395,1947,
%T A258656 2487,3603,4627,6273,8934,12432,15637,20943,29147,37613,50296,67870,
%U A258656 88542,113240,153682,201900,257125,338397,446354,570098,734576,966634,1234879,1574763,2048746,2634002,3322639,4268611
%N A258656 O.g.f.: exp( Sum_{n>=1} A256357(n^2)*x^n/n ), where exp( Sum_{n>=1} A256357(n)*x^n/n )  =  1 + Sum_{n>=1} x^(n^2) + x^(2*n^2).
%H A258656 Paul D. Hanna, <a href="/A258656/b258656.txt">Table of n, a(n) for n = 0..1000</a>
%e A258656 G.f.: A(x) = 1 + x + 3*x^2 + 5*x^3 + 2*x^4 + 10*x^5 + 13*x^6 + 23*x^7 +...
%e A258656 where
%e A258656 log(A(x)) = x + 5*x^2/2 + 7*x^3/3 - 19*x^4/4 + 21*x^5/5 + 59*x^6/6 + 57*x^7/7 - 115*x^8/8 + 61*x^9/9 + 145*x^10/10 +...+ A256357(n^2)*x^n/n +...
%o A258656 (PARI) {A258655(n) = local(L=x); L = log(1 + sum(k=1, n+1, x^(k^2) + x^(2*k^2)) +x*O(x^(n^2))); n^2*polcoeff(L, n^2)}
%o A258656 {a(n) = polcoeff( exp( sum(k=1,n+1, A258655(k)*x^k/k) +x*O(x^n) ), n)}
%o A258656 for(n=1, 121, print1(a(n), ", "))
%o A258656 (PARI) /* Much faster: */
%o A258656 {A258655(n) = -sigma(n^2) + sumdiv(n^2, d, if(d%4==2, d)) + 2*sumdiv(n^2, d, if((d%8)%3==1, d))}
%o A258656 {a(n) = polcoeff( exp( sum(k=1,n+1, A258655(k)*x^k/k) +x*O(x^n) ), n)}
%o A258656 for(n=1,121, print1(a(n), ", "))
%Y A258656 Cf. A258655, A256357.
%K A258656 nonn
%O A258656 0,3
%A A258656 _Paul D. Hanna_, Jun 06 2015