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 A111597 Lah numbers: a(n) = n!*binomial(n-1,6)/7!. 4
 1, 56, 2016, 60480, 1663200, 43908480, 1141620480, 29682132480, 779155977600, 20777492736000, 565147802419200, 15721384321843200, 448059453172531200, 13097122477350912000, 392913674320527360000, 12101741169072242688000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 7,2 REFERENCES Louis Comtet, Advanced Combinatorics, Reidel, 1974, p. 156. John Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 44. LINKS G. C. Greubel, Table of n, a(n) for n = 7..440 FORMULA E.g.f.: ((x/(1-x))^7)/7!. a(n) = (n!/7!)*binomial(n-1, 7-1). If we define f(n,i,x) = Sum_{k=i..n} (Sum_{j=i..k} (binomial(k,j)*Stirling1(n,k)* Stirling2(j,i)*x^(k-j) ) ) then a(n+1) = (-1)^n*f(n,6,-8), (n>=6). - Milan Janjic, Mar 01 2009 From Amiram Eldar, May 02 2022: (Start) Sum_{n>=7} 1/a(n) = 6342*(Ei(1) - gamma) - 8988*e + 80374/5, where Ei(1) = A091725, gamma = A001620, and e = A001113. Sum_{n>=7} (-1)^(n+1)/a(n) = 170142*(gamma - Ei(-1)) - 101640/e - 490714/5, where Ei(-1) = -A099285. (End) MATHEMATICA k = 7; a[n_] := n!*Binomial[n-1, k-1]/k!; Table[a[n], {n, k, 22}] (* Jean-François Alcover, Jul 09 2013 *) PROG (Magma) [Factorial(n-7)*Binomial(n, 7)*Binomial(n-1, 6): n in [7..30]]; // G. C. Greubel, May 10 2021 (Sage) [factorial(n-7)*binomial(n, 7)*binomial(n-1, 6) for n in (7..30)] # G. C. Greubel, May 10 2021 CROSSREFS Column 7 of A008297 and unsigned A111596. Column 6 of A001778. Cf. A001113, A001620, A091725, A099285. Sequence in context: A103726 A332859 A004387 * A111781 A221398 A280803 Adjacent sequences: A111594 A111595 A111596 * A111598 A111599 A111600 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Aug 23 2005 STATUS approved

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Last modified September 14 06:05 EDT 2024. Contains 375911 sequences. (Running on oeis4.)