The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A163650 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A163650

Subswing - the inverse binomial transform of the swinging factorial (A056040).
(history; published version)

#16 by R. J. Mathar at Tue Jul 04 08:51:10 EDT 2023

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editing

approved

#15 by R. J. Mathar at Tue Jul 04 08:51:02 EDT 2023

FORMULA

D-finite with recurrence n*a(n) +5*(n-1)*a(n-1) +(n-4)*a(n-2) +(-13*n+23)*a(n-3) +6*(n-3)*a(n-4)=0. - R. J. Mathar, Jul 04 2023

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approved

editing

#14 by Vaclav Kotesovec at Tue Oct 31 05:02:13 EDT 2017

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editing

approved

#13 by Vaclav Kotesovec at Tue Oct 31 05:02:07 EDT 2017

FORMULA

a(n) ~ -(-1)^n * sqrt(n) * 3^(n - 1/2) / (2*sqrt(Pi)). - Vaclav Kotesovec, Oct 31 2017

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approved

editing

#12 by Alois P. Heinz at Tue Aug 01 14:19:18 EDT 2017

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proposed

approved

#11 by G. C. Greubel at Tue Aug 01 14:16:09 EDT 2017

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proposed

#10 by G. C. Greubel at Tue Aug 01 14:15:56 EDT 2017

LINKS

G. C. Greubel, <a href="/A163650/b163650.txt">Table of n, a(n) for n = 0..1000</a>

FORMULA

a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k)*(k!/(floor(k/2)!)^2). - G. C. Greubel, Aug 01 2017

PROG

(PARI) for(n=0, 50, print1(sum(k=0, n, (-1)^(n-k)*binomial(n, k)*(k!/((k\2)!)^2)), ", ")) \\ G. C. Greubel, Aug 01 2017

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approved

editing

#9 by Bruno Berselli at Fri Jun 28 08:37:12 EDT 2013

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proposed

approved

#8 by Jean-François Alcover at Fri Jun 28 06:59:06 EDT 2013

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proposed

#7 by Jean-François Alcover at Fri Jun 28 06:58:59 EDT 2013

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-François Alcover, Jun 28 2013 *)

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approved

editing