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A123954
Expansion of g.f.: x^5/((1-3*x)*(1-4*x)*(1-5*x)*(1 - 8*x + 13*x^2)).
1
0, 0, 0, 0, 1, 20, 244, 2352, 19725, 150996, 1084600, 7438112, 49268857, 317763732, 2007173532, 12470499600, 76456454725, 463727364692, 2787905507488, 16639142746368, 98709193239921, 582627136604436, 3424383528301252
OFFSET
1,6
FORMULA
a(n) = 20*a(n-1) -156*a(n-2) +592*a(n-3) -1091*a(n-4) +780*a(n-5).
a(n) = (4^n -3^n -3*5^(n-1))/12 + (4*A153594(n+1) -19*A153594(n))/78. [Mar 28 2010]
MAPLE
seq(coeff(series(x^5/((1-3*x)*(1-4*x)*(1-5*x)*(1-8*x+13*x^2)), x, n+1), x, n), n = 1..30); # G. C. Greubel, Aug 05 2019
MATHEMATICA
Rest@ CoefficientList[ Series[ x^5/(1 - 20*x + 156*x^2 - 592*x^3 + 1091*x^4 - 780*x^5), {x, 0, 30}], x] (* Harvey P. Dale, Mar 09 2011 *)
PROG
(PARI) my(x='x+O('x^30)); concat([0, 0, 0, 0], Vec(x^5/((1-3*x)*(1-4*x)*(1-5*x)*(1-8*x+13*x^2)))) \\ G. C. Greubel, Aug 05 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); [0, 0, 0, 0] cat Coefficients(R!( x^5/((1-3*x)*(1-4*x)*(1-5*x)*(1-8*x+13*x^2)) )); // G. C. Greubel, Aug 05 2019
(Sage) a=(x^5/((1-3*x)*(1-4*x)*(1-5*x)*(1-8*x+13*x^2))).series(x, 30).coefficients(x, sparse=False); a[1:] # G. C. Greubel, Aug 05 2019
(GAP) a:=[0, 0, 0, 0, 1];; for n in [6..30] do a[n]:=20*a[n-1]-156*a[n-2] +592*a[n-3]-1091*a[n-4]+780*a[n-5]; od; a; # G. C. Greubel, Aug 05 2019
CROSSREFS
Cf. A153594.
Sequence in context: A138442 A341196 A140124 * A125432 A278673 A055757
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009
Definition replaced by Voznyy's generating function of Jul 2009 - the Assoc. Eds of the OEIS, Mar 28 2010
STATUS
approved