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

%I #7 Mar 30 2024 02:33:16

%S 1,2,2,16,44,248,2136,13536,116448,1075392,13066560,136385280,

%T 1811975040,23777683200,354509003520,5632664970240,93712140103680,

%U 1631567291719680,30968760551178240,605247894280028160,12515132360676556800,274444506310599475200

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

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

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

%Y Cf. A007838, A032297, A371547.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Mar 27 2024