A188480 a(n) = (n^4 + 16*n^3 + 65*n^2 + 26*n + 12)/12.

1, 10, 39, 99, 203, 366, 605, 939, 1389, 1978, 2731, 3675, 4839, 6254, 7953, 9971, 12345, 15114, 18319, 22003, 26211, 30990, 36389, 42459, 49253, 56826, 65235, 74539, 84799, 96078, 108441, 121955, 136689, 152714, 170103, 188931

Offset

0,2

Comments

Third column of number triangle A188461.

Links

Vincenzo Librandi, 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.: (1 + 5*x - x^2 - 6*x^3 + 3*x^4)/(1-x)^5.

E.g.f.: exp(x)*(12 + 108*x + 120*x^2 + 22*x^3 + x^4)/12. - Stefano Spezia, Sep 06 2023

Mathematica

Table[(n^4+16n^3+65n^2+26n+12)/12, {n, 0, 40}] (* or *) LinearRecurrence[ {5, -10, 10, -5, 1}, {1, 10, 39, 99, 203}, 40] (* Harvey P. Dale, Jan 23 2016 *)

Prog

(Magma) [(n^4+16*n^3+65*n^2+26*n+12)/12: n in [0..90]]; // Vincenzo Librandi, Apr 05 2011
(PARI) a(n)=1+(n^4+16*n^3+65*n^2+26*n)/12 \\ Charles R Greathouse IV, May 04 2011

Crossrefs

Cf. A188461.

Sequence in context: A360669 A022277 A348617 * A059722 A267748 A229325

Adjacent sequences: A188477 A188478 A188479 * A188481 A188482 A188483

Keyword

nonn,easy

Author

Paul Barry, Apr 01 2011

Status

approved