A163943 Third left hand column of triangle A163940.

0, 3, 17, 52, 121, 240, 428, 707, 1102, 1641, 2355, 3278, 4447, 5902, 7686, 9845, 12428, 15487, 19077, 23256, 28085, 33628, 39952, 47127, 55226, 64325, 74503, 85842, 98427, 112346, 127690, 144553, 163032, 183227, 205241, 229180, 255153

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

G.f.: x*(3 + 2*x - 3*x^2 + x^3)/(1-x)^5.

a(n)= (2*n + 45*n^2 + 22*n^3 + 3*n^4)/24.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).

E.g.f.: (1/24)*x*(72 + 132*x + 40*x^2 + 3*x^3)*exp(x). - G. C. Greubel, Aug 13 2017

Mathematica

LinearRecurrence[{5, -10, 10, -5, 1}, {0, 3, 17, 52, 121}, 40] (* Harvey P. Dale, Feb 25 2017 *)

Prog

(PARI) x='x+O('x^50); concat([0], Vec(x*(3 +2*x -3*x^2 +x^3)/(1-x)^5)) \\ G. C. Greubel, Aug 13 2017

Crossrefs

Cf. A163972.

Equals the third left hand column of A163940.

A163944 is another left hand column.

Sequence in context: A018691 A332869 A225727 * A093418 A173733 A294134

Adjacent sequences: A163940 A163941 A163942 * A163944 A163945 A163946

Keyword

easy,nonn

Author

Johannes W. Meijer, Aug 13 2009

Status

approved