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A163650 Subswing - the inverse binomial transform of the swinging factorial (A056040). 8
1, 0, 1, 2, -9, 44, -165, 594, -2037, 6824, -22437, 72830, -234047, 746316, -2364947, 7455798, -23405085, 73207728, -228275949, 709906518, -2202557691, 6819616020, -21076580511, 65032888998, -200369138571, 616531573224, -1894784517675, 5816886949874 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Analog to the subfactorial A000166.

LINKS

Table of n, a(n) for n=0..27.

Peter Luschny, Swinging Factorial.

FORMULA

E.g.f.: exp(-x)*BesselI(0,2*x)*(1+x). - Peter Luschny, Aug 26 2012

MAPLE

a := proc(n) local k: add((-1)^(n-k)*binomial(n, k)*(k!/iquo(k, 2)!^2), k=0..n) end:

MATHEMATICA

sf[n_] := n!/Quotient[n, 2]!^2; a[n_] := Sum[(-1)^(n-k)*Binomial[n, k]*sf[k], {k, 0, n}]; Table[a[n], {n, 0, 27}] (* Jean-Fran├žois Alcover, Jun 28 2013 *)

CROSSREFS

Row sums of A163649. Cf. A056040, A000166.

Sequence in context: A020113 A272199 A260074 * A259777 A013981 A216861

Adjacent sequences:  A163647 A163648 A163649 * A163651 A163652 A163653

KEYWORD

sign

AUTHOR

Peter Luschny, Aug 02 2009

STATUS

approved

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Last modified June 24 11:32 EDT 2017. Contains 288697 sequences.