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URL: https://oeis.org/A023043

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A023043
6th differences of factorial numbers.
11
265, 2119, 18806, 183822, 1965624, 22852200, 287250480, 3884393520, 56255149440, 869007242880, 14266826784000, 248112809683200, 4557208289356800, 88166812070937600, 1792259345728051200, 38195370237024000000, 851609625265631232000, 19827505082582765568000
OFFSET
0,1
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
(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
Sequence in context: A202464 A183247 A094795 * A211719 A210120 A266308
KEYWORD
nonn,easy
STATUS
approved