A165281 a(n) = (n+1)*(6*n^4 - 51*n^3 + 161*n^2 - 251*n + 251).

251, 232, 243, 224, 475, 2376, 9107, 26368, 63099, 132200, 251251, 443232, 737243, 1169224, 1782675, 2629376, 3770107, 5275368, 7226099, 9714400, 12844251, 16732232, 21508243, 27316224, 34314875, 42678376, 52597107, 64278368, 77947099

Offset: 0

Author

Paul Curtz, Sep 13 2009

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A157371, A152064.

Programs

Magma

[(n+1)*(6*n^4-51*n^3+161*n^2-251*n+251): n in [0..30]]; // Vincenzo Librandi, Aug 07 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 *)

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