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%I #8 Jan 09 2024 17:25:28
%S 1,2,6,22,92,424,2100,10952,59220,328454,1855548,10630282,61585456,
%T 360139296,2123022032,12603671392,75291625002,452279294266,
%U 2730374221784,16556643025496,100801159909630,615936184506514
%N 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).
%C A variant of sequence A107902 by Michael Somos.
%F G.f. A(x) = Sum_{n>=1} a(n)*x^n satisfies the following formulas.
%F (1) A(x) = x / Sum_{n=-oo, +oo} x^(-n*(n-1)/2) * A(x)^(n*(3*n-1)/2).
%F (2) A(x) = Series_Reversion( x^2/G(x) ) where G(x) is g.f. of A107902.
%e A(x) = x + 2*x^2 + 6*x^3 + 22*x^4 + 92*x^5 + 424*x^6 + 2100*x^7 +...
%o (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))}
%o for(n=1,25, print1(a(n),", "))
%Y Cf. A107902, A107944.
%K nonn
%O 1,2
%A _Paul D. Hanna_, May 28 2005
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