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

Author

Johannes W. Meijer, Aug 13 2009

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A163972.

Equals the third left hand column of A163940.

A163944 is another left hand column.

Programs

Mathematica

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

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

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