A305578 a(n) = Sum_{k=0..n} binomial(n,k)*k!!*(n - k)!!.

1, 2, 6, 18, 64, 230, 936, 3822, 17344, 78354, 389280, 1913010, 10267776, 54235350, 311348352, 1751907150, 10673326080, 63531238050, 408231498240, 2556121021650, 17236028160000, 113006008398150, 796296326031360, 5445783239554350, 39959419088977920, 284127133728611250

Offset

0,2

Comments

Exponential convolution of A006882 with itself.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..730

Eric Weisstein's World of Mathematics, Double Factorial

Index entries for sequences related to factorial numbers

Formula

E.g.f.: (1 + x*exp(x^2/2)*(1 + sqrt(Pi/2)*erf(x/sqrt(2))))^2.

Maple

a:= proc(n) option remember; `if`(n<4, [1, 2, 6, 18][n+1],
      3*n*a(n-2)-2*(n-3)*n*a(n-4))
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Jun 14 2018

Mathematica

Table[Sum[Binomial[n, k] k!! (n - k)!!, {k, 0, n}], {n, 0, 25}]
nmax = 25; CoefficientList[Series[(1 + x Exp[x^2/2] (1 + Sqrt[Pi/2] Erf[x/Sqrt[2]]))^2, {x, 0, nmax}], x] Range[0, nmax]!

Crossrefs

Cf. A000165, A001563, A002866, A006882, A305577.

Sequence in context: A150071 A265945 A007454 * A150072 A150073 A150074

Adjacent sequences: A305575 A305576 A305577 * A305579 A305580 A305581

Keyword

nonn

Author

Ilya Gutkovskiy, Jun 05 2018

Status

approved