A346749 - OEIS

%I #4 Aug 01 2021 16:40:16

%S 1,0,1,2,7,26,124,628,3565,22096,149176,1080868,8372543,68957268,

%T 601351748,5528967282,53416626441,540682811424,5718911631856,

%U 63060992662328,723382253378395,8616075340134868,106374847828850676,1359171823319541070,17946987240664242493

%N E.g.f.: exp( (x * (1 + x) * exp(x) - sinh(x)) / 4 ).

%C Exponential transform of A002620.

%F a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * A002620(k) * a(n-k).

%t nmax = 24; CoefficientList[Series[Exp[(x (1 + x) Exp[x] - Sinh[x])/4], {x, 0, nmax}], x] Range[0, nmax]!

%t a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] Floor[k^2/4] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 24}]

%Y Cf. A002620, A003724, A033462.

%K nonn

%O 0,4

%A _Ilya Gutkovskiy_, Aug 01 2021