A163843 Row sums of triangle A163840.

1, 3, 10, 41, 116, 427, 1240, 4181, 12472, 40091, 121364, 380701, 1160186, 3593969, 10979532, 33785469, 103258800, 316532947, 966976444, 2957131673, 9026437602, 27558146133, 84043120308, 256263107177, 780817641926

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)*i$ 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(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[i], {i, k, n}]; Table[Sum[t[n, k], {k, 0, n}], {n, 0, 50}] (* G. C. Greubel, Aug 06 2017 *)

Crossrefs

Cf. A056040, A163840.

Sequence in context: A137781 A208125 A213108 * A149056 A149057 A149058

Adjacent sequences: A163840 A163841 A163842 * A163844 A163845 A163846

Keyword

nonn

Author

Peter Luschny, Aug 06 2009

Status

approved