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A080954
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E.g.f. exp(5x)/(1-x).
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6
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1, 6, 37, 236, 1569, 10970, 81445, 648240, 5576545, 52142030, 531185925, 5891873300, 70946620225, 923526766050, 12935478240325, 194062691183000, 3105155646818625, 52788408935369750, 950195175533921125
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Binomial transform of A053487. 4th Binomial transform of A000522. Fifth binomial transform of n! = A000142.
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FORMULA
| a(n) = n!Sum{k=0..n, 5^k/k!}
a(n) is the permanent of the n X n matrix with 6's on the diagonal and 1's elsewhere. a(n) = Sum(k=0..n, A008290(n, k)*6^k ). - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Dec 12 2003
Conjecture: -a(n) +(n+5)*a(n-1) +5*(1-n)*a(n-2)=0. - R. J. Mathar, Nov 14 2011
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MAPLE
| F(x):=exp(5*x)/(1-x): f[0]:=F(x): for n from 1 to 20 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=0..18); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 03 2009]
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MATHEMATICA
| With[{nn=20}, CoefficientList[Series[Exp[5x]/(1-x), {x, 0, nn}], x] Range[0, nn]!] (* From Harvey P. Dale, Sep 19 2011 *)
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CROSSREFS
| Cf. A008290, A053486, A010842.
Sequence in context: A154623 A196834 A005389 * A073013 A192238 A140712
Adjacent sequences: A080951 A080952 A080953 * A080955 A080956 A080957
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Feb 26 2003
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