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 A000597 Central factorial numbers. (Formerly M5255 N2287) 2
 36, 820, 7645, 44473, 191620, 669188, 1999370, 5293970, 12728936, 28285400, 58856655, 115842675, 217378200, 391367064, 679524340, 1142659012, 1867463260, 2975110060, 4631998657, 7063027565, 10567817084, 15540347900, 22492529150, 32082258390, 45146587200 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,1 REFERENCES J. Riordan, Combinatorial Identities, Wiley, 1968, p. 217. 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 Vincenzo Librandi, Table of n, a(n) for n = 4..1000 Mircea Merca, A Special Case of the Generalized Girard-Waring Formula J. Integer Sequences, Vol. 15 (2012), Article 12.5.7. Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1). FORMULA E.g.f.: x^4 * (x^5 + 75*x^4 + 603*x^3 + 1065*x^2 + 460*x + 36) / (1-x)^10. a(n) = s(n,n-3)^2-2*s(n,n-4)*s(n,n-2)+2*s(n,n-5)*s(n,n-1)+2*s(n,n-6), where s(n,k) are Stirling numbers of the first kind, A048994. - Mircea Merca, Apr 03 2012 Recurrence: (n-4)*(2*n-7)*(35*n^2 - 49*n + 18)*a(n) = n^2*(2*n-1)*(35*n^2 + 21*n + 4)*a(n-1). - Vaclav Kotesovec, Feb 23 2015 For n>=4, a(n) = (2*n-5)*(2*n-3)*(2*n-1)*(35*n^2+21*n+4) * n! / 45360. - Vaclav Kotesovec, Feb 23 2015 MAPLE 1/(-1+z)^10*(z^5+75*z^4+603*z^3+1065*z^2+460*z+36); seq(stirling1(n, n-3)^2-2*stirling1(n, n-4)*stirling1(n, n-2)+2*stirling1(n, n-5)*stirling1(n, n-1)+2*stirling1(n, n-6), n=0..30); # Mircea Merca, Apr 03 2012 MATHEMATICA CoefficientList[Series[(x^5 + 75*x^4 + 603*x^3 + 1065*x^2 + 460*x + 36)/(1-x)^10, {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Feb 23 2015 *) Table[(2*n-5)*(2*n-3)*(2*n-1)*(35*n^2+21*n+4)*n!/45360, {n, 4, 20}] (* Vaclav Kotesovec, Feb 23 2015 *) LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {36, 820, 7645, 44473, 191620, 669188, 1999370, 5293970, 12728936, 28285400}, 40] (* Vincenzo Librandi, Aug 07 2017 *) CROSSREFS Column 3 of triangle A008955. Sequence in context: A028222 A028216 A028221 * A028214 A028197 A028209 Adjacent sequences:  A000594 A000595 A000596 * A000598 A000599 A000600 KEYWORD nonn AUTHOR STATUS approved

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Last modified April 20 01:34 EDT 2021. Contains 343117 sequences. (Running on oeis4.)