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A105251
a(n) = binomial(n+4,n)*binomial(n+8,n).
1
1, 45, 675, 5775, 34650, 162162, 630630, 2123550, 6370650, 17381650, 43801758, 103169430, 229265400, 484306200, 978496200, 1900457064, 3563356995, 6473226375, 11428041625, 19658764125, 33026723730, 54295634250, 87501228750, 138447123750, 215362192500
OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
FORMULA
G.f.: -(70*x^4+224*x^3+168*x^2+32*x+1)/(x-1)^13. - Colin Barker, Jan 21 2013
From Amiram Eldar, Sep 01 2022: (Start)
Sum_{n>=0} 1/a(n) = 640*Pi^2 - 13925728/2205.
Sum_{n>=0} (-1)^n/a(n) = 640*Pi^2/3 - 90112*log(2)/105 + 471984/1225. (End)
EXAMPLE
a(0): C(0+4,0)*C(0+8,0) = C(4,0)*C(8,0) = 1*1 = 1;
a(10): C(10+4,10)*C(10+8,10) = C(14,10)*(18,10) = 1001*43758 = 43801758.
MATHEMATICA
f[n_] := Binomial[n + 4, n]Binomial[n + 8, n]; Table[ f[n], {n, 0, 22}] (* Robert G. Wilson v, Apr 20 2005 *)
LinearRecurrence[{13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 1}, {1, 45, 675, 5775, 34650, 162162, 630630, 2123550, 6370650, 17381650, 43801758, 103169430, 229265400}, 30] (* Harvey P. Dale, May 19 2024 *)
PROG
(Magma) [Binomial(n+4, n)*Binomial(n+8, n): n in [0..30]]; // Vincenzo Librandi, Jul 31 2015
CROSSREFS
Sequence in context: A160234 A110691 A296540 * A099632 A264138 A293971
KEYWORD
easy,nonn
AUTHOR
Zerinvary Lajos, Apr 14 2005
EXTENSIONS
More terms from Robert G. Wilson v, Apr 20 2005
STATUS
approved