OFFSET
0,1
LINKS
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved