The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A022917

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A022917

Multinomial coefficient n!/ ([n/4]!, [(n+1)/4]!, [(n+2)/4]!, [(n+3)/4]!).
(history; published version)

#30 by Alois P. Heinz at Fri Oct 11 21:12:47 EDT 2019

STATUS

editing

approved

#29 by Alois P. Heinz at Fri Oct 11 21:12:44 EDT 2019

LINKS

Alois P. Heinz, <a href="/A022917/b022917.txt">Table of n, a(n) for n = 0..1000</a>

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approved

editing

#28 by Vaclav Kotesovec at Fri Mar 15 05:16:23 EDT 2019

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editing

approved

#27 by Vaclav Kotesovec at Fri Mar 15 05:16:04 EDT 2019

FORMULA

From Vaclav Kotesovec, Mar 15 2019: (Start)

Recurrence: (n+1)*(n+2)*(n+3)*(4*n^3 + 8*n^2 + 4*n - 1)*a(n) = 8*(2*n^2 + 2*n - 1)*(n^3 + 4*n^2 + 7*n + 3)*a(n-1) + 16*(n-1)*(4*n^4 + 16*n^3 + 16*n^2 + 18*n + 15)*a(n-2) + 128*(n-2)*(n-1)*(2*n^3 + 14*n^2 + 31*n + 18)*a(n-3) + 256*(n-3)*(n-2)*(n-1)*(4*n^3 + 20*n^2 + 32*n + 15)*a(n-4).

a(n) ~ 2^(2*n + 5/2) / (Pi*n)^(3/2). (End)

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approved

editing

#26 by Harvey P. Dale at Wed May 30 13:24:36 EDT 2018

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editing

approved

#25 by Harvey P. Dale at Wed May 30 13:24:33 EDT 2018

MATHEMATICA

Table[n!/Times@@(Floor[Range[n, n+3]/4]!), {n, 0, 30}] (* Harvey P. Dale, May 30 2018 *)

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approved

editing

#24 by R. J. Mathar at Thu Aug 06 05:25:10 EDT 2015

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editing

approved

#23 by R. J. Mathar at Thu Aug 06 05:24:55 EDT 2015

MAPLE

A022917 := proc(n)

n!/floor(n/4)!/floor((n+1)/4)!/floor((n+2)/4)!/floor((n+3)/4)! ;

end proc: # R. J. Mathar, Aug 06 2015

#22 by R. J. Mathar at Thu Aug 06 05:24:24 EDT 2015

FORMULA

Conjecture: -(126*n-1)*(n+3)*(n+2)*(n+1)*a(n) +4*(-208*n^4-51*n^3+793*n^2+376*n-6)*a(n-1) +16*(334*n^3-114*n^2-5*n-369)*a(n-2) +64*(n-2)*(334*n^2+264*n-213)*a(n-3) +768*(n-2)*(n-3)*(42*n^2+153*n+113)*a(n-4) +1024*(208*n+177)*(n-2)*(n-3)*(n-4)*a(n-5)=0. - R. J. Mathar, Aug 06 2015

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approved

editing

#21 by N. J. A. Sloane at Wed May 07 00:17:20 EDT 2014

STATUS

proposed

approved