OFFSET
0,1
COMMENTS
The sequence is the numerators of the fifth column of the array on page 56 of the reference. The denominators are A091137(4)=720.
The sequence is the binomial transform of the quasi-finite 251, -19, 30, -60, 360, 720, 0, 0, 0, 0, ...
The fifth differences are (constant) 720; the fourth differences are 720*n + 360.
REFERENCES
P. Curtz, Integration numerique des systemes differentiels a conditions initiales, C.C.S.A., Arcueil, 1969.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
a(n) mod 10 = A010879(n+1).
a(n+1) - a(n) = A157411(n).
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6).
G.f.: ( 251 - 1274*x + 2616*x^2 - 2774*x^3 + 1901*x^4 ) / (x-1)^6. - R. J. Mathar, Jul 06 2011
MATHEMATICA
Table[(n+1)(6n^4-51n^3+161n^2-251n+251), {n, 0, 30}] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {251, 232, 243, 224, 475, 2376}, 30] (* Harvey P. Dale, Aug 20 2014 *)
PROG
(Magma) [(n+1)*(6*n^4-51*n^3+161*n^2-251*n+251): n in [0..30]]; // Vincenzo Librandi, Aug 07 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Sep 13 2009
STATUS
approved