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A331978 E.g.f.: -log(2 - cosh(x)) (even powers only).

%I A331978 #14 Jun 06 2022 07:15:23
%S A331978 0,1,4,46,1114,46246,2933074,263817646,31943268634,5009616448246,
%T A331978 987840438629794,239217148602642046,69790939492563608554,
%U A331978 24143849395162438623046,9772368696995766705116914,4575221153658910691872135246,2453303387149157947685779986874
%N A331978 E.g.f.: -log(2 - cosh(x)) (even powers only).
%F A331978 a(0) = 0; a(n) = A094088(n) - (1/n) * Sum_{k=1..n-1} binomial(2*n,2*k) * A094088(n-k) * k * a(k).
%F A331978 a(n) ~ (2*n)! / (n * log(2 + sqrt(3))^(2*n)). - _Vaclav Kotesovec_, Feb 07 2020
%p A331978 ptan := proc(n) option remember;
%p A331978     if irem(n, 2) = 0 then 0 else
%p A331978     add(`if`(k=0, 1, binomial(n, k)*ptan(n - k)), k = 0..n-1, 2) fi end:
%p A331978 A331978 := n -> ptan(2*n - 1):
%p A331978 seq(A331978(n), n = 0..16);  # _Peter Luschny_, Jun 06 2022
%t A331978 nmax = 16; Table[(CoefficientList[Series[-Log[2 - Cosh[x]], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
%Y A331978 Cf. A000111, A000182, A000629, A003703, A003704, A003707, A094088, A331611.
%K A331978 nonn
%O A331978 0,3
%A A331978 _Ilya Gutkovskiy_, Feb 03 2020