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A354550
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Expansion of e.g.f. exp( x * exp(x^2/2) ).
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6
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1, 1, 1, 4, 13, 46, 241, 1156, 6889, 44668, 300241, 2328976, 18390901, 159273544, 1461200833, 13995753136, 144068872081, 1531949061136, 17259159775969, 202543867724608, 2474236899786781, 31633380519660256, 417760492214548561, 5751414293905728064
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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(n) = n! * Sum_{k=0..floor(n/2)} (n - 2*k)^k/(2^k * k! * (n - 2*k)!).
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MATHEMATICA
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With[{nn=30}, CoefficientList[Series[Exp[x Exp[x^2/2]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Mar 03 2024 *)
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PROG
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(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*(exp(x^2/2)))))
(PARI) a(n) = n!*sum(k=0, n\2, (n-2*k)^k/(2^k*k!*(n-2*k)!));
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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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