A293615 a(n) = Pochhammer(n, 5) / 2.

0, 60, 360, 1260, 3360, 7560, 15120, 27720, 47520, 77220, 120120, 180180, 262080, 371280, 514080, 697680, 930240, 1220940, 1580040, 2018940, 2550240, 3187800, 3946800, 4843800, 5896800, 7125300, 8550360, 10194660, 12082560, 14240160, 16695360, 19477920, 22619520

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 (6,-15,20,-15,6,-1).

Formula

a(n) = n*(n+1)*(n+2)*Stirling2(4 + n, 3 + n).

-a(-n-4) = a(n) for n >= 0.

a(n) = 60*A000389(n+4). - G. C. Greubel, Nov 20 2017

From Colin Barker, Nov 21 2017: (Start)

G.f.: 60*x / (1 - x)^6.

a(n) = (1/2)*(n*(1 + n)*(2 + n)*(3 + n)*(4 + n)).

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>5.

(End)

Maple

A293615 := n -> pochhammer(n, 5)/2:
seq(A293615(n), n=0..11);

Mathematica

LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 60, 360, 1260, 3360, 7560}, 32]
Table[Pochhammer[n, 5]/2, {n, 0, 50}] (* G. C. Greubel, Nov 20 2017 *)

Prog

(PARI) for(n=0, 30, print1(n*(n+1)*(n+2)*stirling(4 + n, 3 + n, 2), ", ")) \\ G. C. Greubel, Nov 20 2017
(Magma) [0] cat [Factorial(n+4)/(2*Factorial(n-1)): n in [1..30]]; // G. C. Greubel, Nov 20 2017
(PARI) concat(0, Vec(60*x / (1 - x)^6 + O(x^40))) \\ Colin Barker, Nov 21 2017

Crossrefs

Cf. A265609, A293475, A293476, A293608.

Sequence in context: A262385 A326051 A024184 * A119631 A269048 A056428

Adjacent sequences: A293612 A293613 A293614 * A293616 A293617 A293618

Keyword

nonn,easy

Author

Peter Luschny, Oct 20 2017

Status

approved