A090948 a(n) = (1/24)*(n+1)*(n+6)*(n^3+26*n^2+225*n+636).

0, 159, 518, 1198, 2358, 4200, 6974, 10983, 16588, 24213, 34350, 47564, 64498, 85878, 112518, 145325, 185304, 233563, 291318, 359898, 440750, 535444, 645678, 773283, 920228, 1088625, 1280734, 1498968, 1745898, 2024258, 2336950, 2687049, 3077808

Offset

-1,2

Links

G. C. Greubel, Table of n, a(n) for n = -1..1000

P. Erdos, R. K. Guy and J. W. Moon, On refining partitions, J. London Math. Soc., 9 (1975), 565-570.

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

Formula

G.f.: (159-436*x+475*x^2-240*x^3+47*x^4)/(1-x)^6. - Colin Barker, Sep 10 2012

E.g.f.: (3816 +8616*x +3852*x^2 +636*x^3 +43*x^4 +x^5)*exp(x)/24. - G. C. Greubel, Feb 04 2019

Maple

A090948:=n->(n+1)*(n+6)*(n^3+26*n^2+225*n+636)/24; seq(A090948(n), n=-1..100); # Wesley Ivan Hurt, Dec 12 2013

Mathematica

Table[(n+1)(n+6)(n^3+26n^2+225n+636)/24, {n, -1, 100}] (* Wesley Ivan Hurt, Dec 12 2013 *)
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 159, 518, 1198, 2358, 4200}, 40] (* Harvey P. Dale, Jan 16 2015 *)

Prog

(PARI) a(n) = (n+1)*(n+6)*(n^3+26*n^2+225*n+636)/24; \\ Altug Alkan, Jan 10 2015
(Magma) [(n+1)*(n+6)*(n^3+26*n^2+225*n+636)/24: n in [-1..30]]; // G. C. Greubel, Feb 04 2019
(Sage) [(n+1)*(n+6)*(n^3+26*n^2+225*n+636)/24 for n in (-1..30)] # G. C. Greubel, Feb 04 2019
(GAP) List([-1..30], n -> (n+1)*(n+6)*(n^3+26*n^2+225*n+636)/24); # G. C. Greubel, Feb 04 2019

Crossrefs

Sequence in context: A329535 A250659 A280971 * A242115 A227709 A212780

Adjacent sequences: A090945 A090946 A090947 * A090949 A090950 A090951

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 28 2004

Status

approved