A163844 Row sums of triangle A163841.

1, 5, 25, 125, 621, 3065, 15051, 73645, 359485, 1752125, 8532591, 41537105, 202200415, 984526275, 4795673085, 23372376525, 113978687085, 556205251325, 2716129289775, 13273197773125, 64909884686595, 317652752793975, 1555587408645225, 7623031579626625

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Peter Luschny, Swinging Factorial.

Formula

a(n) = Sum_{k=0..n} Sum_{i=k..n} binomial(n-k,n-i)*(2i)$ where i$ denotes the swinging factorial of i (A056040).

Maple

swing := proc(n) option remember; if n = 0 then 1 elif
irem(n, 2) = 1 then swing(n-1)*n else 4*swing(n-1)/n fi end:
a := proc(n) local i, k; add(add(binomial(n-k, n-i)*swing(2*i), i=k..n), k=0..n) end:

Mathematica

sf[n_] := n!/Quotient[n, 2]!^2; t[n_, k_] := Sum[Binomial[n - k, n - i]*sf[2*i], {i, k, n}]; Table[Sum[t[n, k], {k, 0, n}], {n, 0, 50}] (* G. C. Greubel, Aug 06 2017 *)

Crossrefs

Cf. A056040, A163841.

Sequence in context: A370144 A269772 A269652 * A250357 A216125 A057831

Adjacent sequences: A163841 A163842 A163843 * A163845 A163846 A163847

Keyword

nonn

Author

Peter Luschny, Aug 06 2009

Status

approved