|
| |
|
|
A005460
|
|
a(n) = (3*n+4)*(n+3)!/24.
(Formerly M4433)
|
|
4
|
|
|
|
1, 7, 50, 390, 3360, 31920, 332640, 3780000, 46569600, 618710400, 8821612800, 134399865600, 2179457280000, 37486665216000, 681734237184000, 13071512982528000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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R. Austin, R. K. Guy, and R. Nowakowski, unpublished notes, circa 1987.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R. Austin, R. K. Guy, & R. Nowakowski, Unpublished notes, 1987
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
John K. Sikora, On Calculating the Coefficients of a Polynomial Generated Sequence Using the Worpitzky Number Triangles, arXiv:1806.00887 [math.NT], 2018.
|
|
|
FORMULA
|
G.f.: (1+2x) / (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
|
|
|
CROSSREFS
|
Cf. A028246.
Sequence in context: A081189 A108869 A065429 * A053155 A266432 A267243
Adjacent sequences: A005457 A005458 A005459 * A005461 A005462 A005463
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
N. J. A. Sloane.
|
|
|
STATUS
|
approved
|
| |
|
|
