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A053529
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n! * number of partitions of n.
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9
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1, 1, 4, 18, 120, 840, 7920, 75600, 887040, 10886400, 152409600, 2235340800, 36883123200, 628929100800, 11769069312000, 230150688768000, 4833164464128000, 105639166144512000, 2464913876705280000, 59606099200327680000, 1525429559126753280000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Commuting permutations: number of ordered pairs g, h in Symm(n) such that gh = hg.
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REFERENCES
| R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.12, solution.
R. P. Stanley, Pairs with equal squares, Problem 10654, Amer. Math. Monthly, 107 (April 2000), solution p. 368.
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FORMULA
| E.g.f: sum(n>=0, x^n/prod(k=1,n,1-x^k)) = exp(sum(n>=1, 1/n*x^n/(1-x^n))) - Joerg Arndt, Jan 29 2011
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MAPLE
| seq(count(Permutation(n))*count(Partition(n)), n=1..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 16 2006
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PROG
| (PARI) Vec(serlaplace(exp(sum(k=1, 55, x^k/(1-x^k)/k)))) [From Joerg Arndt, Apr 16 2010]
(PARI) Vec(serlaplace(sum(n=0, 55, x^n/prod(k=1, n, 1-x^k)))) [From Joerg Arndt, Jan 29 2011]
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CROSSREFS
| Cf. A000041, A072169, A079860.
Sequence in context: A141714 A137567 A162224 * A005442 A084661 A112294
Adjacent sequences: A053526 A053527 A053528 * A053530 A053531 A053532
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 16 2000
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