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A351423
Expansion of e.g.f. -log(1 - log(1 + log(1 + log(1 + log(1+x))))).
2
1, -3, 16, -124, 1270, -16243, 249776, -4494334, 92716855, -2158505443, 55996266046, -1602132913687, 50124833578256, -1702501170925098, 62391472267252322, -2453892459756494459, 103101294099324376489, -4608723131704380915202
OFFSET
1,2
FORMULA
a(n) = T(n,5), T(n,k) = Sum_{j=1..n} Stirling1(n,j) * T(j,k-1), k>1, T(n,1) = (n-1)!.
MATHEMATICA
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, 5]; Array[a, 18] (* Amiram Eldar, Feb 11 2022 *)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(-log(1-log(1+log(1+log(1+log(1+x)))))))
(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, 5);
CROSSREFS
Column k=5 of A351420.
Sequence in context: A005119 A190291 A090135 * A188417 A327826 A157457
KEYWORD
sign
AUTHOR
Seiichi Manyama, Feb 11 2022
STATUS
approved