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A278428
Series reversion of g.f. (1/2)*x*(-1; -x)_inf, where (a; q)_inf is the q-Pochhammer symbol.
6
1, 1, 1, 2, 6, 17, 46, 128, 373, 1119, 3405, 10464, 32478, 101781, 321642, 1023512, 3276326, 10543100, 34088806, 110690682, 360810160, 1180195810, 3872588051, 12743937024, 42049240694, 139082885503, 461072582522, 1531697761470, 5098246648103, 17000237006441
OFFSET
1,4
COMMENTS
(1/2)*x*(-1; -x)_inf is the g.f. for A081360 shifted right.
LINKS
Eric Weisstein's World of Mathematics, q-Pochhammer Symbol.
FORMULA
a(n) ~ c * d^n / n^(3/2), where c = 0.1211369424750398272226454930396... and d = A318204 = 3.509754327949703340437273523375193698454789733931739911... - Vaclav Kotesovec, Nov 23 2016
MATHEMATICA
InverseSeries[x QPochhammer[-1, -x]/2 + O[x]^35][[3]]
(* Calculation of constant c: *) 1/Sqrt[(4/s^2 - s*Derivative[0, 2][QPochhammer][-1, -s]/r) * Pi] /. FindRoot[{2*r == s*QPochhammer[-1, -s], 2*r == s^2*Derivative[0, 1][QPochhammer][-1, -s]}, {r, 1/3}, {s, 1/2}, WorkingPrecision -> 120] (* Vaclav Kotesovec, Oct 03 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved