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A005460
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a(n) = (3*n+4)*(n+3)!/24.
(Formerly M4433)
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5
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1, 7, 50, 390, 3360, 31920, 332640, 3780000, 46569600, 618710400, 8821612800, 134399865600, 2179457280000, 37486665216000, 681734237184000, 13071512982528000, 263564384219136000, 5575400435404800000, 123469776914964480000, 2856835183101419520000
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OFFSET
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0,2
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COMMENTS
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Essentially Stirling numbers of second kind - third external diagonal of Worpitzky triangle A028246.
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REFERENCES
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R. Austin, R. K. Guy, and R. Nowakowski, unpublished notes, circa 1987.
R. K. Guy, personal communication.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..300
R. Austin, R. K. Guy, and R. Nowakowski, Unpublished notes, 1987
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
Rajesh Kumar Mohapatra and Tzung-Pei Hong, On the Number of Finite Fuzzy Subsets with Analysis of Integer Sequences, Mathematics (2022) Vol. 10, No. 7, 1161.
John K. Sikora, On Calculating the Coefficients of a Polynomial Generated Sequence Using the Worpitzky Number Triangles, arXiv:1806.00887 [math.NT], 2018.
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FORMULA
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E.g.f.: (1+2*x)/(1-x)^5.
a(n) = S2(n+3, n+1)*n! = n!*A001296(n+1). - Olivier Gérard, Sep 13 2016
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MATHEMATICA
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Table[StirlingS2[n + 3, n + 1]*n!, {n, 0, 20}]
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PROG
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(MAGMA) [(3*n+4)*Factorial(n+3)/24: n in [0..20]]; // Vincenzo Librandi, Oct 08 2011
(PARI) a(n)=(3*n+4)*(n+3)!/24 \\ Charles R Greathouse IV, Jun 30 2017
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CROSSREFS
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Cf. A028246.
Sequence in context: A108869 A065429 A346846 * A053155 A266432 A267243
Adjacent sequences: A005457 A005458 A005459 * A005461 A005462 A005463
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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