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A351891
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Expansion of e.g.f. exp( sinh(sqrt(2)*x) / sqrt(2) ).
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1
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1, 1, 1, 3, 9, 25, 105, 443, 1969, 10609, 57265, 338547, 2190969, 14498185, 104277849, 784965803, 6150938593, 51229928929, 440694547681, 3967606065891, 37247506348905, 361022009762809, 3645855348771273, 38001754007842715, 409302848055407761, 4558828622414199121
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OFFSET
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0,4
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LINKS
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FORMULA
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a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} binomial(n-1,2*k) * 2^k * a(n-2*k-1).
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MATHEMATICA
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nmax = 25; CoefficientList[Series[Exp[Sinh[Sqrt[2] x]/Sqrt[2]], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, 2 k] 2^k a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 25}]
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CROSSREFS
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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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