A058985 6 + 33 n + 6 binomial(n, 2) - 28 binomial(n, 3) + 20 binomial(n, 4) - 47 binomial(n, 5).

6, 39, 78, 95, 82, 4, -248, -904, -2362, -5235, -10398, -19035, -32686, -53294, -83252, -125450, -183322, -260893, -362826, -494469, -661902, -871984, -1132400, -1451708, -1839386, -2305879, -2862646, -3522207, -4298190, -5205378, -6259756, -7478558

Offset

0,1

Comments

Obtained by simply fitting a fifth degree polynomial to the terms 6,39,78,95,82,4 (see A058897).

Links

Harry J. Smith, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

a(n) = 6 + 94/15*n + 183/4*n^2 - 187/8*n^3 + 19/4*n^4 - 47/120*n^5.

G.f.: (6+3*x-66*x^2+92*x^3-8*x^4-74*x^5)/(1-x)^6. [Colin Barker, Apr 23 2012]

Mathematica

CoefficientList[Series[(6+3x-66x^2+92x^3-8x^4-74x^5)/(1-x)^6, {x, 0, 40}], x] (* or *) LinearRecurrence[ {6, -15, 20, -15, 6, -1}, {6, 39, 78, 95, 82, 4}, 40] (* Harvey P. Dale, Sep 14 2024 *)

Prog

(PARI) { for (n = 0, 200, a=6 + 33*n + 6*binomial(n, 2) - 28*binomial(n, 3) + 20*binomial(n, 4) - 47*binomial(n, 5); write("b058985.txt", n, " ", a); ) } \\ Harry J. Smith, Jun 24 2009

Crossrefs

Cf. A058897.

Sequence in context: A253803 A355412 A058897 * A116951 A163737 A354728

Adjacent sequences: A058982 A058983 A058984 * A058986 A058987 A058988

Keyword

sign,easy,changed

Author

N. J. A. Sloane, Jan 17 2001

Status

approved