A334157 Row sums of array A158777.

1, 2, 5, 16, 89, 686, 5917, 54860, 588401, 7370074, 103522421, 1573237832, 25869057865, 462768222086, 8965777751309, 186025937645956, 4106375449878497, 96241703493486770, 2390797380938894821, 62730027061416412544

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = n!*Sum_{k=0..n} A003269(k+1)/(n-k)!.

a(n) = n!*Sum_{k=0..n} Sum_{s=0..floor(k/3)} binomial(k-3*s, s)/(n-k)!.

E.g.f.: exp(x)/(1 - x - x^4).

Maple

W := proc(n, m) local v, s, h; v := 0;
for s from 0 to m do
if 0 = (m - s) mod 4 then
h := (m - s)/4;
v := v + binomial(n - s - 3*h, h)/s!;
end if; end do; n!*v; end proc;
seq(add(W(n1, m1), m1 = 0 .. n1), n1 = 0 .. 35);

Mathematica

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 *)

Crossrefs

Cf. A003269, A087208, A158777, A330044, A330045.

Sequence in context: A048754 A176343 A327062 * A306020 A357341 A037075

Adjacent sequences: A334154 A334155 A334156 * A334158 A334159 A334160

Keyword

nonn

Author

Petros Hadjicostas, Apr 16 2020

Status

approved