A278428 Series reversion of g.f. (1/2)*x*(-1; -x)_inf, where (a; q)_inf is the q-Pochhammer symbol.

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

Vaclav Kotesovec, Table of n, a(n) for n = 1..1000

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

Cf. A081360, A109085, A171805, A181315, A255526.

Sequence in context: A005592 A346169 A102403 * A344433 A356934 A200379

Adjacent sequences: A278425 A278426 A278427 * A278429 A278430 A278431

Keyword

nonn

Author

Vladimir Reshetnikov, Nov 21 2016

Status

approved