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A337420
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a(n) = Sum_{k=0..n} (-n)^(n-k) * binomial(2*k,k) * binomial(2*n,2*k).
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2
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1, 1, -14, -7, 1222, -14873, 26196, 3522955, -110841786, 2088947819, -15869398244, -823790768205, 55262757020956, -2199333670723343, 65894251730104552, -1235877788883794355, -18904175519674543546, 3743957841955101437667, -268850524243738610546292, 14826380281246309472525851
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..19.
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MATHEMATICA
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a[n_] := Sum[If[n == 0, Boole[n == k], (-n)^(n - k)] * Binomial[2*k, k] * Binomial[2*n, 2*k], {k, 0, n}]; Array[a, 20, 0] (* Amiram Eldar, Aug 27 2020 *)
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PROG
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(PARI) {a(n) = sum(k=0, n, (-n)^(n-k)*binomial(2*k, k)*binomial(2*n, 2*k))}
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CROSSREFS
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Main diagonal of A337419.
Cf. A337388.
Sequence in context: A040185 A033964 A275337 * A154037 A248600 A240245
Adjacent sequences: A337417 A337418 A337419 * A337421 A337422 A337423
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KEYWORD
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sign
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AUTHOR
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Seiichi Manyama, Aug 27 2020
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STATUS
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approved
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