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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
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
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
Sequence in context: A264867 A354832 A115725 * A196630 A079572 A053391
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jun 05 2018
STATUS
approved

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Last modified May 23 05:11 EDT 2024. Contains 372758 sequences. (Running on oeis4.)