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A293608
a(n) = (3*n + 7)*Pochhammer(n, 5) / 4!.
5
0, 50, 390, 1680, 5320, 13860, 31500, 64680, 122760, 218790, 370370, 600600, 939120, 1423240, 2099160, 3023280, 4263600, 5901210, 8031870, 10767680, 14238840, 18595500, 24009700, 30677400, 38820600, 48689550, 60565050, 74760840, 91626080, 111547920, 134954160
OFFSET
0,2
FORMULA
a(n) = n*(n+1)*Stirling2(4 + n, 2 + n).
-a(-n-4) = a(n) - 30*binomial(n+4, 5)*(n + 2) for n >= 0.
From Colin Barker, Nov 21 2017: (Start)
G.f.: 10*x*(5 + 4*x) / (1 - x)^7.
a(n) = (1/24)*(n*(168 + 422*n + 395*n^2 + 175*n^3 + 37*n^4 + 3*n^5)).
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>6.
(End)
MAPLE
A293608 := n -> (3*n+7)*pochhammer(n, 5)/4!:
seq(A293608(n), n=0..11);
MATHEMATICA
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 50, 390, 1680, 5320, 13860, 31500}, 32]
Table[n*(n+1)*StirlingS2[4 + n, 2 + n], {n, 0, 50}] (* G. C. Greubel, Nov 20 2017 *)
f[n_] := (3 n + 7) Pochhammer[n, 5]/4!; Array[f, 31, 0] (* or *)
CoefficientList[ Series[10x (5 + 4x)/(1 - x)^7, {x, 0, 30}], x] (* Robert G. Wilson v, Nov 21 2017 *)
PROG
(PARI) for(n=0, 30, print1(n*(n+1)*stirling(4 + n, 2 + n, 2), ", ")) \\ G. C. Greubel, Nov 20 2017
(Magma) [0] cat [(3*n + 7)*Factorial(n+4)/(Factorial(4)*Factorial(n-1)): n in [1..30]]; // G. C. Greubel, Nov 20 2017
(PARI) concat(0, Vec(10*x*(5 + 4*x) / (1 - x)^7 + O(x^40))) \\ Colin Barker, Nov 21 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter Luschny, Oct 20 2017
STATUS
approved