A247481 G.f. A(x) satisfies: x = Sum_{n>=1} 1/A(x)^n * Product_{k=1..n} (1 - 1/A(x)^(2*k-1)).

1, 1, -1, -1, -2, -14, -98, -822, -7948, -86590, -1046916, -13892842, -200653570, -3133064534, -52596852266, -944892417438, -18091297436248, -367841660947508, -7916992964642992, -179849204152350892, -4300928485463624458, -108013481381638292266

Offset

0,5

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..370

Formula

a(n) ~ c * 12^n * n^n / (exp(n) * Pi^(2*n)), where c = -2*sqrt(6)/(Pi*exp(Pi^2/8)) = -0.45411558500969644... - Vaclav Kotesovec, Dec 01 2014, updated Aug 22 2017

Mathematica

nmax = 20; aa = ConstantArray[0, nmax]; aa[[1]] = 1; Do[AGF = 1+Sum[aa[[n]]*x^n, {n, 1, j-1}]+koef*x^j; sol=Solve[SeriesCoefficient[Sum[Product[(1-1/AGF^(2m-1))/AGF, {m, 1, k}], {k, 1, j}], {x, 0, j}]==0, koef][[1]]; aa[[j]]=koef/.sol[[1]], {j, 2, nmax}]; Flatten[{1, aa}]

Crossrefs

Cf. A247482 (exponent=0), A249934 (exponent=3), A214692 (exponent=4), A247480 (exponent=5), A214693 (exponent=6), A214694 (exponent=8), A214695 (exponent=10).

Cf. A214690, A214670.

Sequence in context: A322262 A109808 A304444 * A037516 A037719 A158811

Adjacent sequences: A247478 A247479 A247480 * A247482 A247483 A247484

Keyword

sign

Author

Vaclav Kotesovec, Dec 01 2014

Status

approved