A107902 Expansion coefficients of the solution of a functional equation.

1, 2, 2, 2, 4, 12, 32, 72, 148, 318, 772, 2014, 5216, 13060, 32168, 80176, 204714, 531054, 1380492, 3574768, 9247262, 24023702, 62819630, 165074070, 434726670, 1145890266, 3024348486, 7999762500, 21214170582, 56378759128, 150069876570

Offset

1,2

Links

Table of n, a(n) for n=1..31.

Formula

G.f. A(x) satisfies A(x) = x * f(x, A(x)) where f(, ) is Ramanujan's general theta function.

Example

G.f. = x + 2*x^2 + 2*x^3 + 2*x^4 + 4*x^5 + 12*x^6 + 32*x^7 + 72*x^8 + ...

Prog

(PARI) {a(n) = my(A); if( n<1, 0, A = x + O(x^2); for(k=2, n, A = x * sum(i= -sqrtint(n-1), sqrtint(n+2), x^((i^2+i)/2) * A^((i^2-i)/2))); polcoeff(A, n))};

Crossrefs

Sequence in context: A131562 A260786 A067920 * A142974 A259856 A279805

Adjacent sequences: A107899 A107900 A107901 * A107903 A107904 A107905

Keyword

nonn

Author

Michael Somos, May 26 2005

Status

approved