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Search: id:A000274
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| A000274 |
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Number of permutations of length n by rises.
(Formerly M3048 N1236)
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+0
7
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| 1, 3, 18, 110, 795, 6489, 59332, 600732, 6674805, 80765135, 1057289046, 14890154058, 224497707343, 3607998868005, 61576514013960, 1112225784377144, 21197714949305577, 425131949816628507, 8950146311929021210
(list; graph; listen)
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OFFSET
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3,2
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REFERENCES
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F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 263.
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 210 (divided by 2).
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FORMULA
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a(n) = (1 + n) a(n - 1) + (3 + n) a(n - 2) + (3 - n) a(n - 3) + (2 - n) a(n - 4).
E.g.f.: x^2/2*exp(-x)/(1-x)^2. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Jan 03 2003
a(n)=(n-1)^2/(n-2)*a(n-1)-(-1)^n*(n-1)/2, n>2, a(2)=0. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Aug 31 2003
(1/2){[n!/e] - [(n-1)!/e]} (conjectured).
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MAPLE
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a:=n->sum(n!*sum((-1)^k/k!/2, j=1..n), k=0..n): seq(a(n), n=2..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 17 2007
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CROSSREFS
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Cf. A010027, A000255, A000166, A000313, A001260, A001261.
A diagonal in triangle A010027.
Sequence in context: A074571 A114311 A134092 this_sequence A054122 A074566 A113328
Adjacent sequences: A000271 A000272 A000273 this_sequence A000275 A000276 A000277
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KEYWORD
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easy,nonn
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AUTHOR
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njas, Simon Plouffe (plouffe(AT)math.uqam.ca)
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