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A334157 Row sums of array A158777.

%I A334157 #19 Apr 17 2020 03:06:57
%S A334157 1,2,5,16,89,686,5917,54860,588401,7370074,103522421,1573237832,
%T A334157 25869057865,462768222086,8965777751309,186025937645956,
%U A334157 4106375449878497,96241703493486770,2390797380938894821,62730027061416412544
%N A334157 Row sums of array A158777.
%F A334157 a(n) = n!*Sum_{k=0..n} A003269(k+1)/(n-k)!.
%F A334157 a(n) = n!*Sum_{k=0..n} Sum_{s=0..floor(k/3)} binomial(k-3*s, s)/(n-k)!.
%F A334157 E.g.f.: exp(x)/(1 - x - x^4).
%p A334157 W := proc(n, m) local v, s, h; v := 0;
%p A334157 for s from 0 to m do
%p A334157 if 0 = (m - s) mod 4 then
%p A334157 h := (m - s)/4;
%p A334157 v := v + binomial(n - s - 3*h, h)/s!;
%p A334157 end if; end do; n!*v; end proc;
%p A334157 seq(add(W(n1, m1), m1 = 0 .. n1), n1 = 0 .. 35);
%t A334157 Table[Apply[Plus, CoefficientList[Expand[t^n*n!*SeriesCoefficient[Series[Exp[t*x]/( 1 - x/t - t^4*x^4), {x, 0, 50}], n]], t]], {n, 0, 40}]; (* Program due to _Roger L. Bagula_ from A158777 *)
%Y A334157 Cf. A003269, A087208, A158777, A330044, A330045.
%K A334157 nonn
%O A334157 0,2
%A A334157 _Petros Hadjicostas_, Apr 16 2020