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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

Index entries for sequences related to factorial numbers

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

David W. Wilson

STATUS

approved

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Last modified February 17 18:14 EST 2020. Contains 332005 sequences. (Running on oeis4.)