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A305578 a(n) = Sum_{k=0..n} binomial(n,k)*k!!*(n - k)!!. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 4 09:03 EDT 2020. Contains 336201 sequences. (Running on oeis4.)