A253285 a(n) = RF(n+1,3)*C(n+2,n-1), where RF(a,n) is the rising factorial.

0, 24, 240, 1200, 4200, 11760, 28224, 60480, 118800, 217800, 377520, 624624, 993720, 1528800, 2284800, 3329280, 4744224, 6627960, 9097200, 12289200, 16364040, 21507024, 27931200, 35880000, 45630000, 57493800, 71823024, 89011440, 109498200, 133771200, 162370560

Offset

0,2

Links

Table of n, a(n) for n=0..30.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

G.f.: -24/(x-1)^4 - 144/(x-1)^5 - 240/(x-1)^6 - 120/(x-1)^7. See the comment in A253284 for the general case.

a(n) = n*((n+1)*(n+2))^2*(n+3)/6.

a(n) = (N^3 + 4*N^2 + 4*N)/6 = N*(N + 2)^2/6 with N = n^2 + 3*n.

From Bruno Berselli, Mar 06 2018: (Start)

a(n) = 24*A006542(n+3) for n>0.

a(n) = Sum_{i=0..n} i*(i+1)^3*(i+2). Therefore, the first differences are in A133754. (End)

Maple

seq(n*((n+1)*(n+2))^2*(n+3)/6, n=0..19);

Mathematica

Table[n ((n + 1) (n + 2))^2 (n + 3)/6, {n, 0, 40}] (* Bruno Berselli, Mar 06 2018 *)
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 24, 240, 1200, 4200, 11760, 28224}, 40] (* Harvey P. Dale, Aug 05 2024 *)

Prog

(Sage) [n*((n+1)*(n+2))^2*(n+3)/6 for n in (0..40)] # Bruno Berselli, Mar 06 2018
(GAP) List([0..40], n -> n*((n+1)*(n+2))^2*(n+3)/6); # Bruno Berselli, Mar 06 2018
(Magma) [n*((n+1)*(n+2))^2*(n+3)/6: n in [0..40]]; // Bruno Berselli, Mar 06 2018
(Python) [n*((n+1)*(n+2))**2*(n+3)/6 for n in range(40)] # Bruno Berselli, Mar 06 2018

Crossrefs

Cf. A002378, A006542, A083374, A133754, A253284.

Sequence in context: A192491 A167548 A192849 * A052796 A056269 A000919

Adjacent sequences: A253282 A253283 A253284 * A253286 A253287 A253288

Keyword

nonn,easy

Author

Peter Luschny, Mar 23 2015

Status

approved