# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a278428 Showing 1-1 of 1 %I A278428 #15 Oct 03 2023 03:07:18 %S A278428 1,1,1,2,6,17,46,128,373,1119,3405,10464,32478,101781,321642,1023512, %T A278428 3276326,10543100,34088806,110690682,360810160,1180195810,3872588051, %U A278428 12743937024,42049240694,139082885503,461072582522,1531697761470,5098246648103,17000237006441 %N A278428 Series reversion of g.f. (1/2)*x*(-1; -x)_inf, where (a; q)_inf is the q-Pochhammer symbol. %C A278428 (1/2)*x*(-1; -x)_inf is the g.f. for A081360 shifted right. %H A278428 Vaclav Kotesovec, Table of n, a(n) for n = 1..1000 %H A278428 Eric Weisstein's World of Mathematics, q-Pochhammer Symbol. %F A278428 a(n) ~ c * d^n / n^(3/2), where c = 0.1211369424750398272226454930396... and d = A318204 = 3.509754327949703340437273523375193698454789733931739911... - _Vaclav Kotesovec_, Nov 23 2016 %t A278428 InverseSeries[x QPochhammer[-1, -x]/2 + O[x]^35][[3]] %t A278428 (* 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 *) %Y A278428 Cf. A081360, A109085, A171805, A181315, A255526. %K A278428 nonn %O A278428 1,4 %A A278428 _Vladimir Reshetnikov_, Nov 21 2016 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE