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A037963 a(n) = n^2*(n+1)*(3*n^2 + 7*n - 2)*(n+5)!/11520. 4
0, 1, 126, 5796, 186480, 5103000, 129230640, 3162075840, 76592355840, 1863435974400, 45950224320000, 1155068769254400, 29708792431718400, 783699448602470400, 21234672840116736000, 591499300737945600000 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A292882 A140902 A270512 * A240929 A285172 A208618
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified July 15 19:27 EDT 2024. Contains 374334 sequences. (Running on oeis4.)