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A365013
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E.g.f. satisfies A(x) = exp( x*A(x)/(1 - x * A(x)^3) ).
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3
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1, 1, 5, 58, 1061, 26536, 843457, 32553424, 1478813513, 77304347776, 4571222616701, 301696674682624, 21985118975444077, 1753288356936334336, 151887264799071753785, 14203597499192539334656, 1426051485043745729079953, 153000280727938469281693696
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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} (3*n-2*k+1)^(k-1) * binomial(n-1,n-k)/k!.
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MATHEMATICA
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Array[#!*Sum[ (3 # - 2 k + 1)^(k - 1)*Binomial[# - 1, # - k]/k!, {k, 0, #}] &, 18, 0] (* Michael De Vlieger, Aug 18 2023 *)
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PROG
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(PARI) a(n) = n!*sum(k=0, n, (3*n-2*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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