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A305577 a(n) = Sum_{k=0..n} k!!*(n - k)!!. 2
1, 2, 5, 10, 26, 58, 167, 414, 1324, 3606, 12729, 37674, 145578, 463770, 1944879, 6614190, 29852856, 107616150, 518782545, 1970493210, 10077228270, 40125873690, 216425656215, 899557170750, 5091758227620, 22011865939350, 130202223160905, 583641857191050, 3594820517111250 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Convolution of A006882 with itself.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..807

Eric Weisstein's World of Mathematics, Double Factorial

Index entries for sequences related to factorial numbers

FORMULA

G.f.: (Sum_{k>=0} k!!*x^k)^2.

MAPLE

a:= proc(n) option remember; `if`(n<4, n^2+1,

      ((3*n^2-4*n-2)*a(n-2) +(n+1)*a(n-3)

       -2*a(n-1) -(n-1)^2*n*a(n-4))/(2*n-4))

    end:

seq(a(n), n=0..35);  # Alois P. Heinz, Jun 14 2018

MATHEMATICA

Table[Sum[k!! (n - k)!!, {k, 0, n}], {n, 0, 28}]

nmax = 28; CoefficientList[Series[Sum[k!! x^k, {k, 0, nmax}]^2, {x, 0, nmax}], x]

CROSSREFS

Cf. A003149, A006882, A034430, A059371, A111308, A126674, A305578.

Sequence in context: A212709 A264867 A115725 * A196630 A079572 A053391

Adjacent sequences:  A305574 A305575 A305576 * A305578 A305579 A305580

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jun 05 2018

STATUS

approved

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Last modified July 16 09:13 EDT 2020. Contains 335784 sequences. (Running on oeis4.)