A134528 G.f. A(x) satisfies: 1 = Sum_{n>=0} A(x)^(n+1)*x^n/2^(n*(n-1)/2) where A(x) = Sum_{n>=0} a(n)*x^n/2^(n*(n-1)/2).
1, -1, 3, -21, 319, -10193, 674047, -91369921, 25234490623, -14140806673665, 16031563354478591, -36691986271455923201, 169262051631703928107007, -1571807846118598776606101505, 29353752424684301883376834576383, -1101562988034649825668233119938625537
Offset: 0
Keywords
Examples
A(x) = 1 - x + 3/2*x^2 - 21/8*x^3 + 319/64*x^4 - 10193/1024*x^5 +... 1 = A(x) + A(x)^2*x + A(x)^3*x^2/2 + A(x)^4*x^3/8 + A(x)^5*x^4/64 + ...
Crossrefs
Cf. A118410.
Programs
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PARI
{a(n)=2^(n*(n+1)/2)*polcoeff((1/x)*serreverse(sum(k=1,n+1,x^k/2^(k*(k-1)/2))+O(x^(n+2))),n)}
Formula
G.f.: A(x) = (1/x)*series_reversion[x*Sum_{n>=0} x^n/2^(n*(n-1)/2)].