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A104676
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a(n) = binomial(n+2,2) * binomial(n+7,2).
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2
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21, 84, 216, 450, 825, 1386, 2184, 3276, 4725, 6600, 8976, 11934, 15561, 19950, 25200, 31416, 38709, 47196, 57000, 68250, 81081, 95634, 112056, 130500, 151125, 174096, 199584, 227766, 258825, 292950, 330336, 371184, 415701, 464100, 516600, 573426, 634809, 700986
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OFFSET
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0,1
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LINKS
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FORMULA
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G.f.: 3*( -7+7*x-2*x^2 ) / (x-1)^5. - R. J. Mathar, Nov 29 2015
a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - Wesley Ivan Hurt, Jan 25 2022
Sum_{n>=0} 1/a(n) = 7/100.
Sum_{n>=0} (-1)^n/a(n) = 7/180. (End)
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EXAMPLE
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If n=0 then C(0+2,0+0)*C(0+7,2) = C(2,0)*C(7,2) = 1*21 = 21.
If n=8 then C(8+2,8+0)*C(8+7,2) = C(10,8)*C(15,2) = 45*105 = 4725.
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MAPLE
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MATHEMATICA
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Table[Binomial[n + 2, 2] Binomial[n + 7, 2], {n, 0, 37}] (* Michael De Vlieger, Nov 29 2015 *)
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PROG
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(PARI) a(n) = binomial(n+2, 2)*binomial(n+7, 2); \\ Michel Marcus, Nov 29 2015
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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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STATUS
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approved
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