A305577 a(n) = Sum_{k=0..n} k!!*(n - k)!!.

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

Offset

0,2

Comments

Convolution of A006882 with itself.

Links

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

Poloni, Federico; Del Corso, Gianna M. Counting Fiedler pencils with repetitions. Linear Algebra Appl. 532, 463-499 (2017), corollary 24.

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: A264867 A354832 A115725 * A196630 A079572 A053391

Adjacent sequences: A305574 A305575 A305576 * A305578 A305579 A305580

Keyword

nonn

Author

Ilya Gutkovskiy, Jun 05 2018

Status

approved