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

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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• R. Austin, R. K. Guy, and R. Nowakowski, unpublished notes, circa 1987.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• R. Austin, R. K. Guy, and R. Nowakowski, Unpublished notes, 1987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

Crossrefs

Cf. A028246.

Programs

Magma

[(3*n+4)*Factorial(n+3)/24: n in [0..20]]; // Vincenzo Librandi, Oct 08 2011

Mathematica

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

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

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