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A352617
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Expansion of e.g.f. exp( exp(x) + sinh(x) - 1 ).
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3
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1, 2, 5, 16, 60, 254, 1199, 6206, 34827, 210264, 1355992, 9288954, 67279309, 513149498, 4107383185, 34398823888, 300629113292, 2735356900806, 25857446103571, 253472859754918, 2572266378189583, 26981781750668760, 292136508070103208, 3260640536587635410, 37472102225288489529
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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(0) = 1; a(n) = (1/2) * Sum_{k=1..n} binomial(n-1,k-1) * (3 - (-1)^k) * a(n-k).
a(n) = Sum_{k=0..floor(n/2)} binomial(n,2*k) * A005046(k) * A352279(n-2*k).
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MAPLE
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a:= proc(n) option remember; `if`(n=0, 1, add(
a(n-k)*binomial(n-1, k-1)*(1+(k mod 2)), k=1..n))
end:
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MATHEMATICA
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nmax = 24; CoefficientList[Series[Exp[Exp[x] + Sinh[x] - 1], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = (1/2) Sum[Binomial[n - 1, k - 1] (3 - (-1)^k) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 24}]
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PROG
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(PARI) my(x='x+O('x^30)); Vec(serlaplace(exp( exp(x) + sinh(x) - 1 ))) \\ Michel Marcus, Mar 24 2022
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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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