OFFSET
2,1
REFERENCES
Identity (1.19)/(n+3) in H. W. Gould, Combinatorial Identities, Morgantown, 1972, page 3.
LINKS
G. C. Greubel, Table of n, a(n) for n = 2..350
FORMULA
(n-1)^2*a(n) = n*(n+2)*(n+1)*a(n-1). - R. J. Mathar, Jul 26 2015
From G. C. Greubel, Jun 20 2022: (Start)
a(n) = (1/(n+3))*Sum_{j=0..n} (-1)^(n+j)*binomial(n,j)*j^(n+3).
a(n) = n!*StirlingS2(n+3, n)/(n+3).
a(n) = A037961(n)/(n+3).
a(n) = A131689(n+3, n).
a(n) = A019538(n+3, n).
E.g.f.: x*(1 + 6*x + 3*x^2)/(4*(1-x)^6). (End)
MATHEMATICA
Table[(n+2)!n^2(n+1)/48, {n, 2, 20}] (* Harvey P. Dale, Jul 29 2021 *)
PROG
(Magma) [Factorial(n)*StirlingSecond(n+3, n)/(n+3): n in [2..30]]; // G. C. Greubel, Jun 20 2022
(SageMath) [factorial(n)*stirling_number2(n+3, n)/(n+3) for n in (2..30)] # G. C. Greubel, Jun 20 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved