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 A023043 6th differences of factorial numbers. 9
 265, 2119, 18806, 183822, 1965624, 22852200, 287250480, 3884393520, 56255149440, 869007242880, 14266826784000, 248112809683200, 4557208289356800, 88166812070937600, 1792259345728051200, 38195370237024000000, 851609625265631232000, 19827505082582765568000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets FORMULA From Vaclav Kotesovec, Oct 21 2012: (Start) E.g.f.: (265 + 264*x + 135*x^2 + 40*x^3 + 15*x^4 + x^6)/(1-x)^7. D-finite Recurrence: a(n) = (n+7)*a(n-1) - (n-1)*a(n-2), n>=1. a(n) ~ n!*n^6. (End) MATHEMATICA CoefficientList[Series[-(265 + 264x + 135x^2 + 40x^3 + 15x^4 + x^6)/(x - 1)^7, {x, 0, 20}], x] Range[0, 20]! (* Vaclav Kotesovec, Oct 21 2012 *) Differences[Range[0, 23]!, 6] (* Alonso del Arte, Nov 10 2018 *) PROG (PARI) x='x+O('x^66); Vec(serlaplace( -(265 +264*x +135*x^2 +40*x^3 +15*x^4 +x^6) / (x-1)^7 )) \\ Joerg Arndt, May 04 2013 (GAP) a:=[265, 2119];;  for n in [3..20] do a[n]:=(n+6)*a[n-1]-(n-2)*a[n-2]; od; a; # Muniru A Asiru, Nov 23 2018 (MAGMA) I:=[2119, 18806]; [265] cat [n le 2 select I[n] else (n+7)*Self(n-1) - (n-1)*Self(n-2): n in [1..30]]; // G. C. Greubel, Nov 23 2018 (Sage) f= (265 + 264*x + 135*x^2 + 40*x^3 + 15*x^4 + x^6)/(1-x)^7 g=f.taylor(x, 0, 30) L=g.coefficients() coeffs={c[1]:c[0]*factorial(c[1]) for c in L} coeffs # G. C. Greubel, Nov 23 2018 CROSSREFS Sequence in context: A202464 A183247 A094795 * A211719 A210120 A266308 Adjacent sequences:  A023040 A023041 A023042 * A023044 A023045 A023046 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified January 19 06:37 EST 2020. Contains 331033 sequences. (Running on oeis4.)