A005460 a(n) = (3*n+4)*(n+3)!/24. (Formerly M4433)

1, 7, 50, 390, 3360, 31920, 332640, 3780000, 46569600, 618710400, 8821612800, 134399865600, 2179457280000, 37486665216000, 681734237184000, 13071512982528000, 263564384219136000, 5575400435404800000, 123469776914964480000, 2856835183101419520000

Offset

0,2

Comments

Essentially Stirling numbers of second kind - third external diagonal of Worpitzky triangle A028246.

References

R. Austin, R. K. Guy, and R. Nowakowski, unpublished notes, circa 1987.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).

Links

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R. Austin, R. K. Guy, and R. Nowakowski, Unpublished notes, 1987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.

Formula

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

Mathematica

Table[StirlingS2[n+3, n+1]*n!, {n, 0, 20}]

Prog

(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
(SageMath) [factorial(n)*stirling_number2(n+3, n+1) for n in range(21)] # G. C. Greubel, Nov 22 2022

Crossrefs

Cf. A028246.

Sequence in context: A108869 A065429 A346846 * A053155 A367235 A355171

Adjacent sequences: A005457 A005458 A005459 * A005461 A005462 A005463

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved