A107944 - OEIS

%I #5 Dec 30 2023 16:20:23

%S 1,-2,6,-22,88,-376,1680,-7752,36660,-176758,865676,-4294666,21537584,

%T -109007408,556096920,-2856490080,14761719654,-76693856026,

%U 400359733068,-2098903394904,11045982153266,-58335010518882,309052004994306,-1642074778175370,8748018667952754

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

%C A variant of sequence A107902 by Michael Somos.

%F G.f.: A(x) = series_reversion(G107902(x)) where G107902(x) is g.f. of A107902.

%e A(x) = x - 2*x^2 + 6*x^3 - 22*x^4 + 88*x^5 - 376*x^6 + 1680*x^7 -+...

%o (PARI) {a(n)=local(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))}

%Y Cf. A107902, A107945.

%K sign

%O 1,2

%A _Paul D. Hanna_, May 28 2005