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A188685
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Partial alternating sums of binomial(3n,n)^2/(2n+1)^2.
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10
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1, 0, 9, 135, 2890, 71639, 1967545, 58125959, 1813561210, 59034994415, 1987910416810, 68818255912790, 2437897047570874, 88061136002276310, 3234416650430634090, 120525771933269446806, 4548292982313797644875
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} (-1)^(n-k)*A001764(k)^2.
4*(2*n^2 + 9*n + 10)^2*a(n+2) - (713*n^4 + 4230*n^3 + 9317*n^2 + 9000*n + 3200)*a(n+1) - 9*(9*n^2 + 27*n + 20)^2*a(n) = 0.
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MAPLE
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A001764 := proc(n) binomial(3*n, n)/(2*n+1) ; end proc:
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MATHEMATICA
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Table[Sum[Binomial[3k, k]^2(-1)^(n-k)/(2k+1)^2, {k, 0, n}], {n, 0, 20}]
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PROG
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(Maxima) makelist(sum(binomial(3*k, k)^2*(-1)^(n-k)/(2k+1)^2, k, 0, n), n, 0, 20);
(Magma) [ &+[(-1)^(n-k)*Binomial(3*k, k)^2/(2*k+1)^2: k in [0..n]]: n in [0..16]]; // Bruno Berselli, Apr 11 2011
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CROSSREFS
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Cf. Alternate partial sums of binomial(3n,n)^2/(2n+1)^k: A188680 (k=0), A188683 (k=1), this sequence (k=2).
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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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