|
|
A270272
|
|
a(n) = binomial(n+3,n)^3.
|
|
1
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
|
|
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.
Sum_{n>=0} (-1)^n/a(n) = 1296*log(2) + 405*zeta(3)/2 - 4563/4. - Amiram Eldar, Sep 20 2022
|
|
MAPLE
|
|
|
MATHEMATICA
|
Table[Binomial[n+3, n]^3, {n, 0, 30}]
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|