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A104674
a(n) = binomial(n+6, 6) * binomial(n+11, n).
1
1, 84, 2184, 30576, 286650, 2018016, 11435424, 54609984, 226972746, 840639800, 2824549728, 8730426432, 25099975992, 67725379008, 172768824000, 419252346240, 972796459635, 2167754048460, 4656656844840, 9674494830000, 19494107082450, 38192536324800, 72913023892800
OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (18,-153,816,-3060,8568,-18564,31824,-43758,48620,-43758,31824,-18564,8568,-3060,816,-153,18,-1).
FORMULA
From Amiram Eldar, Aug 30 2022: (Start)
Sum_{n>=0} 1/a(n) = 33033*Pi^2 - 16431490141/50400.
Sum_{n>=0} (-1)^n/a(n) = 1171456*log(2)/105 - 11*Pi^2/2 - 1625274871/211680. (End)
EXAMPLE
If n=0 then C(0+6,6)*C(0+11,0+0) = C(6,6)*C(11,0) = 1*1 = 1.
If n=8 then C(8+6,6)*C(8+11,8+0) = C(14,6)*C(19,8) = 3003*75582 = 226972746.
MATHEMATICA
a[n_] := Binomial[n + 6, 6] * Binomial[n + 11, n]; Array[a, 25, 0] (* Amiram Eldar, Aug 30 2022 *)
PROG
(PARI) a(n)={binomial(n+6, 6) * binomial(n+11, n)} \\ Andrew Howroyd, Nov 08 2019
CROSSREFS
Cf. A062190.
Sequence in context: A098935 A370572 A297486 * A221010 A219584 A140903
KEYWORD
easy,nonn
AUTHOR
Zerinvary Lajos, Apr 22 2005
EXTENSIONS
a(8) corrected and terms a(9) and beyond from Andrew Howroyd, Nov 08 2019
STATUS
approved