A270272 a(n) = binomial(n+3,n)^3.
1, 64, 1000, 8000, 42875, 175616, 592704, 1728000, 4492125, 10648000, 23393656, 48228544, 94196375, 175616000, 314432000, 543338496, 909853209, 1481544000, 2352637000, 3652264000, 5554637011, 8291469824, 12167000000, 17576000000, 25025203125, 35158608576, 48787170264
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
Programs
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Maple
A270272:=n->binomial(n+3,n)^3: seq(A270272(n), n=0..50); # Wesley Ivan Hurt, Jul 17 2017
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Mathematica
Table[Binomial[n+3,n]^3,{n,0,30}] -
PARI
a(n) = binomial(n+3,n)^3; \\ Michel Marcus, Jul 17 2017
Formula
G.f.: 3F2(4,4,4;1,1;z).
G.f.: (1 + 54x + 405x^2 + 760x^3 + 405x^4 + 54x^5 + x^6)/(x-1)^10.
a(n) = (6 + 11n + 6n^2 + n^3)^3/216.
a(n) = A000292(n+1)^3.
Sum_{n>=0} 1/a(n) = 783/4 - 162*zeta(3). - Jaume Oliver Lafont, Jul 17 2017
Sum_{n>=0} (-1)^n/a(n) = 1296*log(2) + 405*zeta(3)/2 - 4563/4. - Amiram Eldar, Sep 20 2022