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A365012
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E.g.f. satisfies A(x) = exp( x*A(x)/(1 - x * A(x)^2) ).
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6
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1, 1, 5, 52, 833, 18116, 498907, 16648402, 653034545, 29450331928, 1501456530131, 85398143019014, 5361130115439529, 368227694339818132, 27468201247134068891, 2211469648218676671466, 191131823105565504395873, 17650493961604405811144624
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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, #}] &, 19, 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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