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A188682
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Partial sums of binomials bin(3n,n)^2/(2n+1).
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9
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1, 4, 49, 1057, 28282, 848101, 27357493, 928760053, 32747441926, 1188869998801, 44174723634526, 1672716549215326, 64340599136306926, 2507814491482180894, 98859670298036582494, 3935425516392739090270, 158006444406545953115743
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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(bin(3*k,k)^2/(2*k+1),k=0..n).
Recurrence: 4*(n+2)^2*(4*n^2+16*n+15) * a(n+2) -(745*n^4+4502*n^3+10181*n^2+10216*n+3840) * a(n+1) +9*(9*n^2+27*n+20)^2 *a(n) = 0.
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MATHEMATICA
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Table[Sum[Binomial[3k, k]^2/(2k+1), {k, 0, n}], {n, 0, 20}]
Accumulate[Table[Binomial[3n, n]^2/(2n+1), {n, 0, 20}]] (* Harvey P. Dale, Jul 10 2016 *)
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PROG
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(Maxima) makelist(sum(binomial(3*k, k)^2/(2k+1), k, 0, n), n, 0, 20);
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CROSSREFS
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Cf. A005809, A001764, A188676, A104859, A188678, A188679, A188680, A188681, A188683, A188684, A188685, A188686, A188687.
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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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