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Search: id:A061206
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| A061206 |
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A diagonal of binomial coefficients multiplied by factorials array. |
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+0
5
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| 1, 10, 90, 840, 8400, 90720, 1058400, 13305600, 179625600, 2594592000, 39956716800, 653837184000, 11333177856000, 207484333056000, 4001483566080000, 81096733605888000, 1723305589125120000
(list; graph; listen)
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OFFSET
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1,2
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LINKS
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Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
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FORMULA
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n*(n+3)!/24
If we define f(n,i,x)= sum(sum(binomial(k,j)*stirling1(n,k)*stirling2(j,i)*x^(k-j),j=i..k),k=i..n) then a(n-3)=(-1)^n*f(n,4,-2), (n>=4). [From Milan R. Janjic (agnus(AT)blic.net), Mar 01 2009]
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EXAMPLE
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a(4)=840 because 4*(7!)/24=4*7*6*5=840.
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MAPLE
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seq(sum(mul(j, j=3..n), k=4..n)/12, n=4..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 01 2007
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MATHEMATICA
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Table[Sum[n!/24, {i, 4, n}], {n, 4, 20}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 12 2009]
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PROGRAM
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(Other) sage: [binomial(n, 4)*factorial (n-3) for n in xrange(4, 21)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 07 2009]
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CROSSREFS
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Cf. A000142, A001563, A001286, A005990, A001339.
Sequence in context: A010576 A003952 A033136 this_sequence A137684 A097394 A063945
Adjacent sequences: A061203 A061204 A061205 this_sequence A061207 A061208 A061209
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KEYWORD
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nonn
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AUTHOR
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Melvin J. Knight (knightmj(AT)juno.com), May 30 2001
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EXTENSIONS
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More terms from Jason Earls (zevi_35711(AT)yahoo.com), Jun 12 2001
Corrected by Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 07 2009
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