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A351424
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a(n) = n! * [x^n] -log(1 - f^(n-1)(x)), where f(x) = log(1+x).
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3
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1, 0, 3, -48, 1270, -50375, 2803829, -208616562, 20003317746, -2402323535658, 353219463307920, -62411008199372327, 13048469028962425266, -3186116313706825820802, 898478811755719496052919, -289795933163271680910773018, 106008143082108931457543700504
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) = T(n,n), T(n,k) = Sum_{j=1..n} Stirling1(n,j) * T(j,k-1), k>1, T(n,1) = (n-1)!.
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MAPLE
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g:= x-> log(1+x):
a:= n-> n! * coeff(series(-log(1-(g@@(n-1))(x)), x, n+1), x, n):
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MATHEMATICA
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T[n_, 1] := (n - 1)!; T[n_, k_] := T[n, k] = Sum[StirlingS1[n, j] * T[j, k - 1], {j, 1, n}]; a[n_] := T[n, n]; Array[a, 16] (* Amiram Eldar, Feb 11 2022 *)
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PROG
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(PARI) T(n, k) = if(k==1, (n-1)!, sum(j=1, n, stirling(n, j, 1)*T(j, k-1)));
a(n) = T(n, n);
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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