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 A001812 Coefficients of Laguerre polynomials. (Formerly M5257 N2289) 3
 1, 36, 882, 18816, 381024, 7620480, 153679680, 3161410560, 66784798080, 1454424491520, 32724551059200, 761589551923200, 18341615042150400, 457129482588979200, 11787410229615820800, 314330939456421888000, 8663746518767628288000, 246661959710796005376000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 5,2 REFERENCES M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 799. C. Lanczos, Applied Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1956, p. 519. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe, Table of n, a(n) for n = 5..100 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy]. C. Lanczos, Applied Analysis (Annotated scans of selected pages) FORMULA a(n) = (-1)*A021009(n, 5), n >= 5. a(n) = ((n!/5!)^2)/(n-5)!, n >= 5. 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)^(n-1)*f(n,5,-6), (n>=5). - Milan Janjic, Mar 01 2009 EXAMPLE G.f. = x^5 + 36*x^6 + 882*x^7 + 18816*x^8 + 381024*x^9 + 7620480*x^10 + ... MATHEMATICA Table[((n!/5!)^2)/(n-5)!, {n, 5, 20}] (* T. D. Noe, Aug 10 2012 *) PROG (Sage) [factorial(m) * binomial(m, 5) / 120 for m in range(5, 23)] # Zerinvary Lajos, Jul 05 2008 (PARI) for(n=5, 20, print1(((n!/5!)^2)/(n-5)!, ", ")) \\ G. C. Greubel, May 11 2018 (MAGMA) [((Factorial(n)/Factorial(5))^2)/Factorial(n-5): n in [5..20]]; // G. C. Greubel, May 11 2018 CROSSREFS Sequence in context: A243569 A145150 A166790 * A229680 A169836 A335220 Adjacent sequences:  A001809 A001810 A001811 * A001813 A001814 A001815 KEYWORD nonn AUTHOR STATUS approved

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Last modified September 27 12:30 EDT 2020. Contains 337380 sequences. (Running on oeis4.)