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A163843 Row sums of triangle A163840. 2
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 (list; graph; refs; listen; history; text; internal format)
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,changed

AUTHOR

Peter Luschny, Aug 06 2009

STATUS

approved

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Last modified August 20 17:05 EDT 2017. Contains 290836 sequences.