A293488 E.g.f.: Product_{m>0} (1 + x^(2*m-1) + x^(4*m-2)/2!).

1, 1, 1, 6, 24, 180, 1080, 10080, 90720, 907200, 10886400, 139708800, 2035756800, 29578348800, 479480601600, 7846046208000, 146459529216000, 2845499424768000, 58421660064768000, 1246862279190528000, 28586598596075520000, 664182248232222720000

Offset: 0

Author

Seiichi Manyama, Oct 10 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..446

Crossrefs

Column k=2 of A293486.

Cf. A293138, A293304.

Programs

PARI

N=66; x='x+O('x^N); Vec(serlaplace(prod(m=1, N, 1+x^(2*m-1)+x^(4*m-2)/2)))

Formula

a(n) ~ 2^(-3/4) * c^(1/4) * exp(sqrt(2*c*n) - n) * n^(n-1/4), where c = -polylog(2, -1/2 - I/2) - polylog(2, -1/2 + I/2) = 0.966945612722157030083754546059357521... - Vaclav Kotesovec, Oct 11 2017