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A000313
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Number of permutations of length n by rises.
(Formerly M3633 N1477)
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7
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1, 4, 30, 220, 1855, 17304, 177996, 2002440, 24474285, 323060540, 4581585866, 69487385604, 1122488536715, 19242660629360, 348933579412440, 6673354706262864, 134252194678935321, 2834212998777523380
(list; graph; refs; listen; history; internal format)
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OFFSET
| 4,2
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REFERENCES
| F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 263.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
| a(n)=(n*(n+1)!/6)*sum((-1)^k/k!, k=0..n)
a(n)=A065087(n+2)/3. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 25 2007
E.g.f.: x^3/3!*exp(-x)/(1-x)^2. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 03 2003
a(n) = round( (exp(-1)*(n+1)!+(-1)^n)*n/6 ) - Mark van Hoeij, Oct 25 2011
G.f.: hypergeom([2, 4],[],x/(x+1))/(x+1)^4 - Mark van Hoeij, Nov 07 2011
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MAPLE
| a:=n->sum((n+1)!*sum((-1)^k/k!/3!, j=1..n), k=0..n): seq(a(n), n=2..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 25 2007
series(hypergeom([2, 4], [], x/(x+1))/(x+1)^4, x=0, 30); - Mark van Hoeij, Nov 07 2011
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CROSSREFS
| Cf. A010027, A000255, A000166, A000274, A001260, A001261.
A diagonal in triangle A010027.
Sequence in context: A134093 A007905 A084976 * A082144 A137971 A052604
Adjacent sequences: A000310 A000311 A000312 * A000314 A000315 A000316
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 03 2003
Formula added by Sean A. Irvine (sairvin(AT)xtra.co.nz), Nov 11 2010
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