OFFSET
1,2
COMMENTS
A variant of sequence A107902 by Michael Somos.
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 28 2005
STATUS
approved