A023043 6th differences of factorial numbers.

265, 2119, 18806, 183822, 1965624, 22852200, 287250480, 3884393520, 56255149440, 869007242880, 14266826784000, 248112809683200, 4557208289356800, 88166812070937600, 1792259345728051200, 38195370237024000000, 851609625265631232000, 19827505082582765568000

Offset: 0

Author

David W. Wilson

Keywords

• nonn
• easy

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

Programs

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

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 *)

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

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

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)