A152100 Expansion of g.f. 1 - 2*x*(-7 - 10*x + x^2)/(x - 1)^4.

1, 14, 76, 218, 472, 870, 1444, 2226, 3248, 4542, 6140, 8074, 10376, 13078, 16212, 19810, 23904, 28526, 33708, 39482, 45880, 52934, 60676, 69138, 78352, 88350, 99164, 110826, 123368, 136822, 151220, 166594, 182976, 200398, 218892, 238490

Offset: 0

Author

N. J. A. Sloane, Sep 21 2009, based on email from R. J. Mathar, Mar 22 2009

Keywords

• nonn
• easy
• changed

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A006071.

Programs

Mathematica

Join[{1},LinearRecurrence[{4,-6,4,-1},{14,76,218,472},40]] (* Harvey P. Dale, Aug 07 2012 *)

Formula

From R. J. Mathar, Sep 22 2009: (Start)

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4), n > 4.

a(n) = 2*n*(8*n^2 + 12*n + 1)/3, n > 0. (End)

E.g.f.: 1 + 2*exp(x)*x*(21 + 36*x + 8*x^2)/3. - Stefano Spezia, Aug 24 2025

Extensions

More terms from R. J. Mathar, Sep 22 2009