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A163773 Row sums of the swinging derangement triangle (A163770). 2
1, 1, 4, 15, -14, 185, -454, 2107, -6194, 22689, -70058, 234971, -734304, 2368379, -7404318, 23417955, -72988938, 228324569, -708982738, 2202742447, -6815736144, 21077285943, -65016664062, 200371842727, -616463969324, 1894794918275, -5816606133674, 17839764136377 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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} (-1)^(n-i)*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((-1)^(n-i)*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[(-1)^(n - i)*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 03 2017 *)

CROSSREFS

Cf. A163770.

Sequence in context: A284119 A290377 A095331 * A210788 A229412 A076349

Adjacent sequences:  A163770 A163771 A163772 * A163774 A163775 A163776

KEYWORD

sign

AUTHOR

Peter Luschny, Aug 05 2009

EXTENSIONS

Terms a(18) onward added by G. C. Greubel, Aug 03 2017

STATUS

approved

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