A037963 a(n) = n^2*(n+1)*(3*n^2 + 7*n - 2)*(n+5)!/11520.

0, 1, 126, 5796, 186480, 5103000, 129230640, 3162075840, 76592355840, 1863435974400, 45950224320000, 1155068769254400, 29708792431718400, 783699448602470400, 21234672840116736000, 591499300737945600000

Offset

0,3

Comments

For n>=1, a(n) is equal to the number of surjections from {1,2,...,n+5} onto {1,2,...,n}. - Aleksandar M. Janjic and Milan Janjic, Feb 24 2007

References

Identity (1.21) in H. W. Gould, Combinatorial Identities, Morgantown, 1972; page 3.

Links

G. C. Greubel, Table of n, a(n) for n = 0..350

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Formula

From G. C. Greubel, Jun 20 2022: (Start)

a(n) = (-1)^n * Sum_{j=0..n} (-1)^j * binomial(n, j)*j^(n+5).

a(n) = n!*StirlingS2(n+5, n).

a(n) = A131689(n+5, n).

a(n) = A019538(n+5, n).

E.g.f.: x*(1 + 52*x + 328*x^2 + 444*x^3 + 120*x^4)/(1-x)^11. (End)

Mathematica

Table[n!*StirlingS2[n+5, n], {n, 0, 30}] (* G. C. Greubel, Jun 20 2022 *)

Prog

(Magma) [Factorial(n)*StirlingSecond(n+5, n): n in [0..30]]; // G. C. Greubel, Jun 20 2022
(SageMath) [factorial(n)*stirling_number2(n+5, n) for n in (0..30)] # G. C. Greubel, Jun 20 2022

Crossrefs

Cf. A000142, A019538, A112494, A131689.

Sequence in context: A292882 A140902 A270512 * A240929 A285172 A208618

Adjacent sequences: A037960 A037961 A037962 * A037964 A037965 A037966

Keyword

nonn

Author

N. J. A. Sloane

Status

approved