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A278934
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a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n,k)*binomial(2*k,k)^2.
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2
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1, 3, 29, 303, 3501, 42663, 538769, 6977547, 92078989, 1232902023, 16700233689, 228356672547, 3147087003201, 43659275921667, 609117615688149, 8539863624592023, 120242239301247309, 1699411957967345127, 24098616839012623769, 342754384909199620803
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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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Recurrence: n^2*a(n) = (13*n^2 - 13*n + 3)*a(n-1) + 29*(n-1)^2*a(n-2) + 15*(n-2)*(n-1)*a(n-3). - Vaclav Kotesovec, Dec 02 2016
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MATHEMATICA
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Table[Sum[(-1)^(n-k)*Binomial[n, k]*Binomial[2*k, k]^2, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Dec 02 2016 *)
Table[(-1)^n*HypergeometricPFQ[{1/2, 1/2, -n}, {1, 1}, 16], {n, 0, 20}] (* Vaclav Kotesovec, Dec 02 2016 *)
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CROSSREFS
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Cf. Sum_{k = 0..n} (-1)^(n-k)*binomial(n, k)*binomial(2*k, k)^m: A002426 (m=1), this sequence (m=2), A276537 (m=3).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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