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A306173 a(n) is the n-th term of the inverse Euler transform of j-> n^(j-1). 4
1, 1, 6, 42, 420, 5155, 77658, 1376340, 28133616, 651317463, 16846515510, 481472570920, 15067838554860, 512473599799551, 18821719654854998, 742395982266536520, 31299550394528466960, 1404629090174946183156, 66851805805525048040334, 3363381327122496643643628 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..200

FORMULA

a(n) ~ (1 - exp(-1)) * n^(n-1). - Vaclav Kotesovec, Oct 08 2019

MAPLE

b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,

      add(binomial(g(i, k)+j-1, j)*b(n-i*j, i-1, k), j=0..n/i)))

    end:

g:= proc(n, k) option remember; k^(n-1)-b(n, n-1, k) end:

a:= n-> g(n$2):

seq(a(n), n=1..21);

MATHEMATICA

b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, Sum[Binomial[g[i, k] + j - 1, j]*b[n - i*j, i - 1, k], {j, 0, n/i}]]];

g[n_, k_] := g[n, k] = k^(n - 1) - b[n, n - 1, k];

a[n_] := g[n, n];

a /@ Range[21] (* Jean-Fran├žois Alcover, Jan 06 2020, after Alois P. Heinz *)

CROSSREFS

Main diagonal of A065177.

Cf. A075147, A316073.

Sequence in context: A052608 A245248 A197712 * A254529 A098461 A284161

Adjacent sequences:  A306170 A306171 A306172 * A306174 A306175 A306176

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jun 23 2018

STATUS

approved

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Last modified May 18 23:31 EDT 2022. Contains 353826 sequences. (Running on oeis4.)