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A152297
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Alternate binomial partial sums of binomial(2n,n)*binomial(3n,n) (A006480).
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2
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1, 5, 79, 1427, 28447, 599435, 13100065, 293737085, 6713171455, 155700711995, 3653740285729, 86561367835805, 2067026079739921, 49689509437820933, 1201321507453119103, 29187308928225658787, 712192597620218620735
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = sum((-1)^(n-k)*binomial(n,k)*binomial(2*k,k)*binomial(3*k,k),k=0..n).
D-finite with recurrence Recurrence: (n+3)^2*a(n+3)-(24*n^2+120*n+149)*a(n+2)-51*(n+2)^2*a(n+1)-26*(n+1)*(n+2)*a(n)=0.
E.g.f.: exp(-x)*F(1/3,2/3;1,1;27*x), where F(a1,a2;b1;z) is a hypergeometric series.
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MATHEMATICA
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Table[Sum[Binomial[n, k]Binomial[2k, k]Binomial[3k, k](-1)^(n-k), {k, 0, n}], {n, 0, 16}]
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PROG
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(Maxima) makelist(sum((-1)^(n-k)*binomial(n, k)*binomial(2*k, k)*binomial(3*k, k), k, 0, n), n, 0, 16);
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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