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

0,1

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)

a(n) = (n^6 + 15*n^5 + 100*n^4 + 355*n^3 + 694*n^2 + 689*n + 265) * n!. - Christian Krause, May 03 2026

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 *)
(* Alternative: *)
Differences[Range[0, 23]!, 6] (* Alonso del Arte, Nov 10 2018 *)

Prog

(PARI) my(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
(SageMath)
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

Cf. A023044, A023045, A023046, A023047.

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