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A157411
a(n) = 30*n^4 - 120*n^3 + 120*n^2 - 19.
4
-19, 11, -19, 251, 1901, 6731, 17261, 36731, 69101, 119051, 191981, 294011, 431981, 613451, 846701, 1140731, 1505261, 1950731, 2488301, 3129851, 3887981, 4776011, 5807981, 6998651, 8363501, 9918731, 11681261, 13668731, 15899501, 18392651
OFFSET
0,1
COMMENTS
These are the numerators in column j=4 of the array in A140825 (reference p. 36).
The other columns in A140825 are represented by A000012, A005408, A140811 and A141530.
The link between these columns is given by the first differences: a(n+1) - a(n) = 30*A141530(n), where 30 = A027760(4) = A027760(3) = A027642(4) = A002445(2), then for j=3, A141530(n+1) - A141530(n) = A140070(2)*A140811(n).
REFERENCES
P. Curtz, Integration numerique des systemes differentiels a conditions initiales, Centre de Calcul Scientifique de l'Armement, Note 12, Arcueil (1969).
FORMULA
a(n)= 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
G.f.: (-19 + 106*x - 264*x^2 + 646*x^3 + 251*x^4)/(1-x)^5.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) + 720. Fourth differences are constant, 720.
MATHEMATICA
Table[30n^4-120n^3+120n^2-19, {n, 0, 40}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {-19, 11, -19, 251, 1901}, 40] (* Harvey P. Dale, Mar 08 2015 *)
PROG
(Magma) [30*n^4 - 120*n^3 + 120*n^2 - 19: n in [0..50]]; // Vincenzo Librandi, Aug 07 2011
(PARI) a(n)=30*n^4-120*n^3+120*n^2-19 \\ Charles R Greathouse IV, Oct 16 2015
CROSSREFS
Sequence in context: A107808 A214422 A141045 * A166525 A083156 A356570
KEYWORD
sign,easy
AUTHOR
Paul Curtz, Feb 28 2009
EXTENSIONS
Edited, one index corrected and extended by R. J. Mathar, Sep 17 2009
STATUS
approved