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
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).
Programs
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Magma
[0] cat [Factorial(n+4)/(2*Factorial(n-1)): n in [1..30]]; // G. C. Greubel, Nov 20 2017
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Maple
A293615 := n -> pochhammer(n, 5)/2: seq(A293615(n), n=0..11);
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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 *) -
PARI
for(n=0,30, print1(n*(n+1)*(n+2)*stirling(4 + n, 3 + n, 2), ", ")) \\ G. C. Greubel, Nov 20 2017
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PARI
concat(0, Vec(60*x / (1 - x)^6 + O(x^40))) \\ Colin Barker, Nov 21 2017
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)
From Amiram Eldar, Aug 31 2025: (Start)
Sum_{n>=1} 1/a(n) = 1/48.
Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/3 - 131/144. (End)