A107945 G.f. A(x) satisfies: A(x) = x*f(A(x),A(x)^2/x) where f(,) is Ramanujan's theta function; i.e., A(x) = x*Sum_{n=-oo,+oo} A(x)^(n*(n+1)/2) * (A(x)^2/x)^(n*(n-1)/2).

1, 2, 6, 22, 92, 424, 2100, 10952, 59220, 328454, 1855548, 10630282, 61585456, 360139296, 2123022032, 12603671392, 75291625002, 452279294266, 2730374221784, 16556643025496, 100801159909630, 615936184506514

Offset

1,2

Comments

A variant of sequence A107902 by Michael Somos.

Links

Table of n, a(n) for n=1..22.

Formula

G.f. A(x) = Sum_{n>=1} a(n)*x^n satisfies the following formulas.

(1) A(x) = x / Sum_{n=-oo, +oo} x^(-n*(n-1)/2) * A(x)^(n*(3*n-1)/2).

(2) A(x) = Series_Reversion( x^2/G(x) ) where G(x) is g.f. of A107902.

Example

A(x) = x + 2*x^2 + 6*x^3 + 22*x^4 + 92*x^5 + 424*x^6 + 2100*x^7 +...

Prog

(PARI) {a(n) = my(A=x); 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^((3*i^2-i)/2))); polcoeff(A, n))}
for(n=1, 25, print1(a(n), ", "))

Crossrefs

Cf. A107902, A107944.

Sequence in context: A130579 A279570 A338748 * A279571 A014330 A225294

Adjacent sequences: A107942 A107943 A107944 * A107946 A107947 A107948

Keyword

nonn

Author

Paul D. Hanna, May 28 2005

Status

approved