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).

1, 1, 3, 5, 2, 10, 13, 23, 43, 57, 66, 96, 183, 229, 375, 509, 619, 883, 1395, 1947, 2487, 3603, 4627, 6273, 8934, 12432, 15637, 20943, 29147, 37613, 50296, 67870, 88542, 113240, 153682, 201900, 257125, 338397, 446354, 570098, 734576, 966634, 1234879, 1574763, 2048746, 2634002, 3322639, 4268611

Offset: 0

Author

Paul D. Hanna, Jun 06 2015

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + 3*x^2 + 5*x^3 + 2*x^4 + 10*x^5 + 13*x^6 + 23*x^7 +...
where
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 +...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A258655, A256357.

Programs

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)}
{a(n) = polcoeff( exp( sum(k=1,n+1, A258655(k)*x^k/k) +x*O(x^n) ), n)}
for(n=1, 121, print1(a(n), ", "))

PARI

/* Much faster: */
{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))}
{a(n) = polcoeff( exp( sum(k=1,n+1, A258655(k)*x^k/k) +x*O(x^n) ), n)}
for(n=1,121, print1(a(n), ", "))