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A163943 Third left hand column of triangle A163940. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 12 10:09 EDT 2020. Contains 335657 sequences. (Running on oeis4.)