A293476 a(n) = ((n + 1)/2)*(n + 2)*Pochhammer(n, 5) / 4!.

0, 15, 180, 1050, 4200, 13230, 35280, 83160, 178200, 353925, 660660, 1171170, 1987440, 3248700, 5140800, 7907040, 11860560, 17398395, 25017300, 35331450, 49092120, 67209450, 90776400, 121095000, 159705000, 208415025, 269336340, 344919330, 437992800, 551806200

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 (8,-28,56,-70,56,-28,8,-1).

Formula

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

-a(-n-4) = (n+4)*abs(Stirling1(n+3, n)) for n >= 0.

-a(-n-4) = a(n) + 5*binomial(n+4, 5)*(n+2) for n >= 0.

From Colin Barker, Nov 21 2017: (Start)

G.f.: 15*x*(1 + 4*x + 2*x^2) / (1 - x)^8.

a(n) = (1/48)*(n*(2 + 3*n + n^2)^2*(12 + 7*n + n^2)).

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>7.

(End)

Maple

A293476 := n -> ((n+1)/2)*(n+2)*pochhammer(n, 5)/4!:
seq(A293476(n), n=0..11);

Mathematica

LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {0, 15, 180, 1050, 4200, 13230, 35280, 83160}, 32]
Table[n*StirlingS2[4 + n, 1 + n], {n, 0, 50}] (* G. C. Greubel, Nov 20 2017 *)

Prog

(PARI) for(n=0, 30, print1(n*stirling(n+4, n+1, 2), ", ")) \\ G. C. Greubel, Nov 20 2017
(Magma) [0] cat [((n + 1)/2)*(n + 2)*Factorial(n+4)/(Factorial(4)*Factorial(n-1)): n in [1..30]]; // G. C. Greubel, Nov 20 2017
(PARI) concat(0, Vec(15*x*(1 + 4*x + 2*x^2) / (1 - x)^8 + O(x^40))) \\ Colin Barker, Nov 21 2017

Crossrefs

Cf. A265609, A293475, A293608, A293615.

Sequence in context: A016216 A244604 A001717 * A004992 A055084 A005461

Adjacent sequences: A293473 A293474 A293475 * A293477 A293478 A293479

Keyword

nonn,easy

Author

Peter Luschny, Oct 20 2017

Status

approved