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A105252
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a(n) = binomial(n+5,n)*binomial(n+9,n).
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1
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1, 60, 1155, 12320, 90090, 504504, 2312310, 9060480, 31286970, 97337240, 277411134, 733649280, 1818838840, 4261894560, 9502285320, 20271542016, 41572498275, 82281899700, 157706974425, 293570877600, 532097215650, 941124327000, 1627522854750, 2756636064000
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OFFSET
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0,2
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).
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FORMULA
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G.f.: -(126*x^5+630*x^4+840*x^3+360*x^2+45*x+1)/(x-1)^15. - Colin Barker, Jan 21 2013
Sum_{n>=0} 1/a(n) = 7425*Pi^2/2 - 114902691/3136.
Sum_{n>=0} (-1)^n/a(n) = 28960047/15680 - 255*Pi^2/4 - 12288*log(2)/7. (End)
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EXAMPLE
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a(0): C(0+5,0)*C(0+9,0) = C(5,0)*C(9,0) = 1*1 = 1;
a(10): C(10+5,10)*C(10+9,10) = C(15,10)*(19,10) = 3003*92378 = 277411134.
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MATHEMATICA
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f[n_] := Binomial[n + 5, n]Binomial[n + 9, n]; Table[ f[n], {n, 0, 20}] (* Robert G. Wilson v, Apr 20 2005 *)
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PROG
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(Magma) [Binomial(n+5, n)*Binomial(n+9, n): n in [0..30]]; // Vincenzo Librandi, Jul 31 2015
(Python)
A105252_list, m = [], [2002, -4433, 3487, -1133, 127, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
for _ in range(10**2):
for i in range(14):
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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