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A365016
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E.g.f. satisfies A(x) = exp( x*A(x)^3/(1 - x * A(x)^2) ).
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2
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1, 1, 9, 160, 4345, 159796, 7434199, 418864426, 27732988609, 2110729489048, 181587635465671, 17426825999144926, 1845855944285411425, 213900244312057975348, 26919356609721984494311, 3656322063766897691641666, 533110345129065969043548289
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = n! * Sum_{k=0..n} (2*n+k+1)^(k-1) * binomial(n-1,n-k)/k!.
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MATHEMATICA
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Array[#!*Sum[ (2 # + k + 1)^(k - 1)*Binomial[# - 1, # - k]/k!, {k, 0, #}] &, 17, 0] (* Michael De Vlieger, Aug 18 2023 *)
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PROG
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(PARI) a(n) = n!*sum(k=0, n, (2*n+k+1)^(k-1)*binomial(n-1, n-k)/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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