A371548 Expansion of e.g.f. Product_{k>=1} (1 + 2*x^k/k).

1, 2, 2, 16, 44, 248, 2136, 13536, 116448, 1075392, 13066560, 136385280, 1811975040, 23777683200, 354509003520, 5632664970240, 93712140103680, 1631567291719680, 30968760551178240, 605247894280028160, 12515132360676556800, 274444506310599475200

Offset: 0

Author

Ilya Gutkovskiy, Mar 27 2024

Keywords

• nonn

Crossrefs

Cf. A007838, A032297, A371547.

Programs

Mathematica

nmax = 21; CoefficientList[Series[Product[(1 + 2 x^k/k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!

Formula

a(n) ~ n! * n / (2*exp(2*gamma)), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Mar 28 2024