A346746 - OEIS

%I #5 Aug 01 2021 16:39:58

%S 1,0,1,1,5,12,58,220,1145,5684,33284,198412,1306355,8945046,65658392,

%T 503505600,4076565489,34442610648,304577372128,2802673411280,

%U 26840614943667,266644080930194,2745669007978680,29243006731749200,321810005123384617,3653558357684804324

%N E.g.f.: exp( (x * exp(x) - sinh(x)) / 2 ).

%C Exponential transform of A004526.

%F a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * A004526(k) * a(n-k).

%t nmax = 25; CoefficientList[Series[Exp[(x Exp[x] - Sinh[x])/2], {x, 0, nmax}], x] Range[0, nmax]!

%t a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] Floor[k/2] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 25}]

%Y Cf. A000248, A003724, A004526, A346747, A346748.

%K nonn

%O 0,5

%A _Ilya Gutkovskiy_, Aug 01 2021