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A061206
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A diagonal of binomial coefficients multiplied by factorials array.
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5
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1, 10, 90, 840, 8400, 90720, 1058400, 13305600, 179625600, 2594592000, 39956716800, 653837184000, 11333177856000, 207484333056000, 4001483566080000, 81096733605888000, 1723305589125120000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..300
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
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FORMULA
| 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]
E.g.f.: x/(1-x)^5. (This was initiated by e-mail exchange with Gary Detlefs.) [From Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), May 28 2010]
a(n)= (n+4!/6 * sum((k+2)!/(k+4)!,k=1..n) [From Gary Detlefs (gdetlefs(AT)aol.com), Aug 05 2010]
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EXAMPLE
| a(4)=840 because 4*(7!)/24=4*7*6*5=840.
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MAPLE
| 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
| Table[Sum[n!/24, {i, 4, n}], {n, 4, 20}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 12 2009]
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PROG
| (Other) sage: [binomial(n, 4)*factorial (n-3) for n in xrange(4, 21)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 07 2009]
(MAGMA) [n*Factorial(n+3)/24: n in [1..20]]; // Vincenzo Librandi, Oct 11 2011
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CROSSREFS
| Cf. A000142, A001563, A001286, A005990, A001339.
Sequence in context: A170691 A003952 A033136 * A199527 A137684 A097394
Adjacent sequences: A061203 A061204 A061205 * A061207 A061208 A061209
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KEYWORD
| nonn
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AUTHOR
| Melvin J. Knight (knightmj(AT)juno.com), May 30 2001
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EXTENSIONS
| 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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