A335627 - OEIS

%I #21 Oct 03 2020 03:57:28

%S 1,1,4,20,152,1216,13264,145760,2031872,28617856,480749824,8243878400,

%T 162085486592,3262756228096,73483961257984,1695754607421440,

%U 42992308610957312,1118097332524711936,31487163119164063744,910421423509984378880,28187970433553669292032,896242635855128514789376

%N Expansion of e.g.f. Product_{k>0} 1/(1-tan(x)^k).

%H Vaclav Kotesovec, <a href="/A335627/b335627.txt">Table of n, a(n) for n = 0..200</a>

%F E.g.f.: exp( Sum_{k>0} sigma(k)*tan(x)^k/k ).

%t nmax = 25; CoefficientList[Series[Product[1/(1 - Tan[x]^k), {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Oct 03 2020 *)

%o (PARI) N=40; x='x+O('x^N); Vec(serlaplace(1/eta(tan(x))))

%o (PARI) N=40; x='x+O('x^N); Vec(serlaplace(1/prod(k=1, N, 1-tan(x)^k)))

%o (PARI) N=40; x='x+O('x^N); Vec(serlaplace(exp(sum(k=1, N, sigma(k)*tan(x)^k/k))))

%Y Cf. A000041, A000182, A335626, A335630.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Oct 02 2020