A177399 O.g.f.: exp( Sum_{n>=1} (sigma(2n)-sigma(n))^n * x^n/n ).

1, 2, 10, 188, 1414, 53596, 2923652, 44668152, 651967302, 605335444140, 7564881098284, 157357140966472, 96537385644719004, 695895399853879448, 86358988630956719304, 1103071610291574716763120

Offset: 0

Author

Paul D. Hanna, May 30 2010

Keywords

• nonn

Comments

Here sigma(n) = A000203(n) is the sum of divisors of n.

Compare g.f. to the formula for Jacobi theta_4(x) given by:

. theta_4(x) = exp( Sum_{n>=1} -(sigma(2n)-sigma(n))*x^n/n )

where theta_4(x) = 1 + Sum_{n>=1} 2*(-x)^(n^2).

Examples

			G.f.: A(x) = 1 + 2*x + 10*x^2 + 188*x^3 + 1414*x^4 + 53596*x^5 +...
log(A(x)) = 2*x + 4^2*x^2/2 + 8^3*x^3/3 + 8^4*x^4/4 + 12^5*x^5/5 +...+ A054785(n)^n*x^n/n +...
		

Crossrefs

Cf. A054785, A000203, A177398, A155200.

Programs

PARI

{a(n)=polcoeff(exp(sum(m=1,n,(sigma(2*m)-sigma(m))^m*x^m/m)+x*O(x^n)),n)}