A293475 a(n) = (3*n + 4)*Pochhammer(n, 4) / 4!.

0, 7, 50, 195, 560, 1330, 2772, 5250, 9240, 15345, 24310, 37037, 54600, 78260, 109480, 149940, 201552, 266475, 347130, 446215, 566720, 711942, 885500, 1091350, 1333800, 1617525, 1947582, 2329425, 2768920, 3272360, 3846480, 4498472, 5236000, 6067215, 7000770

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*Stirling2(3 + n, 1 + n).

-a(-n-3) = (n + 3)*abs(Stirling1(n+2, n)) for n >= 0.

-a(-n-3) = a(n) + binomial(n+3, 4) for n >= 0.

From Colin Barker, Nov 21 2017: (Start)

G.f.: x*(7 + 8*x) / (1 - x)^6.

a(n) = n*(24 + 62*n + 57*n^2 + 22*n^3 + 3*n^4)/24.

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

A293475 := n -> (3*n + 4)*pochhammer(n, 4)/4!:
seq(A293475(n), n=0..32);

Mathematica

LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 7, 50, 195, 560, 1330}, 32]
Table[n*StirlingS2[n+3, n+1], {n, 0, 50}] (* G. C. Greubel, Nov 20 2017 *)
f[n_] := (3n + 4) Pochhammer[n, 4]/4!; Array[f, 35, 0] (* or *)
CoefficientList[ Series[ x (7 + 8x)/(1 - x)^6, {x, 0, 34}], x] (* Robert G. Wilson v, Nov 21 2017 *)

Prog

(PARI) for(n=0, 30, print1(n*Stirling(n+3, n+1, 2), ", ")) \\ G. C. Greubel, Nov 20 2017
(Magma) [0] cat [(3*n + 4)*Factorial(n+3)/(Factorial(n-1)*Factorial(4)): n in [1..30]]; // G. C. Greubel, Nov 20 2017
(PARI) concat(0, Vec(x*(7 + 8*x) / (1 - x)^6 + O(x^40))) \\ Colin Barker, Nov 21 2017

Crossrefs

Cf. A265609, A293476, A293608, A293615.

Sequence in context: A368113 A271623 A153693 * A293801 A227676 A278875

Adjacent sequences: A293472 A293473 A293474 * A293476 A293477 A293478

Keyword

nonn,easy

Author

Peter Luschny, Oct 20 2017

Status

approved