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A163773 Row sums of the swinging derangement triangle (A163770). 1
1, 1, 4, 15, -14, 185, -454, 2107, -6194, 22689, -70058, 234971, -734304, 2368379, -7404318, 23417955, -72988938, 228324569 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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).

LINKS

Table of n, a(n) for n=0..17.

Peter Luschny, Swinging Factorial.

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:

CROSSREFS

Cf. A163770

Sequence in context: A126601 A284119 A095331 * A210788 A229412 A076349

Adjacent sequences:  A163770 A163771 A163772 * A163774 A163775 A163776

KEYWORD

sign

AUTHOR

Peter Luschny, Aug 05 2009

STATUS

approved

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Last modified May 23 16:25 EDT 2017. Contains 286925 sequences.