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 A037961 a(n) = n^2*(n+1)*(n+3)!/48. 6
 0, 1, 30, 540, 8400, 126000, 1905120, 29635200, 479001600, 8083152000, 142702560000, 2637143308800, 50999300352000, 1031319184896000, 21785854970880000, 480178027929600000, 11029155770400768000 (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+3} onto {1,2,...,n}. - Aleksandar M. Janjic and Milan Janjic, Feb 24 2007 REFERENCES Identity (1.19) in H. W. Gould, Combinatorial Identities, Morgantown, 1972; page 3. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..400 H. W. Gould, ed. J. Quaintance, Combinatorial Identities, May 2010 (section 10, p.45) Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets FORMULA (n-1)^2*a(n) - n*(n+3)*(n+1)*a(n-1) = 0. - R. J. Mathar, Jul 26 2015 E.g.f.: x*(1 + 8*x + 6*x^2)/(1 - x)^7. - Ilya Gutkovskiy, Feb 20 2017 a(n) = Sum_{k = 0..n} (-1)^(n-k)*binomial(n,k)*k^(n+3). - Peter Bala, Mar 28 2017 From G. C. Greubel, Jun 20 2022: (Start) a(n) = n!*StirlingS2(n+3, n). a(n) = A131689(n+3, n). a(n) = A019538(n+3, n). (End) MATHEMATICA Table[n!*StirlingS2[n+3, n], {n, 0, 30}] (* G. C. Greubel, Jun 20 2022 *) PROG (PARI) a(n)=(n+3)!*n^2*(n+1)/48 \\ Charles R Greathouse IV, Nov 02 2011 (Magma) [Factorial(n+3)*n^2*(n+1)/48: n in [0..20]]; // Vincenzo Librandi, Nov 18 2011 (SageMath) [factorial(n)*stirling_number2(n+3, n) for n in (0..30)] # G. C. Greubel, Jun 20 2022 CROSSREFS Cf. A000142, A001286, A001297, A019538, A037960, A131689. Sequence in context: A270499 A286975 A139626 * A143399 A293103 A075510 Adjacent sequences: A037958 A037959 A037960 * A037962 A037963 A037964 KEYWORD nonn,easy AUTHOR N. J. A. Sloane STATUS approved

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Last modified August 6 07:30 EDT 2024. Contains 374960 sequences. (Running on oeis4.)