A347726 Expansion of e.g.f.: exp(x / (1-x)^x).

1, 1, 1, 7, 37, 221, 1801, 15709, 157641, 1775521, 21898801, 296379931, 4346295757, 68682481141, 1163591541113, 21024039322441, 403559222086801, 8199021870113985, 175746277620520417, 3963144157484213359, 93778090395227788021, 2323080237693908254381

Offset: 0

Author

Seiichi Manyama, Sep 11 2021

Keywords

• nonn

Crossrefs

Cf. A007113, A202152.

Programs

Mathematica

a[0] = 1; a[n_] := n! * Sum[(-1)^(n - i) * Sum[i^j * StirlingS1[n - i - j, j]/(n - i - j)!, {j, 0, n - i}]/i!, {i, 1, n}]; Array[a, 20, 0] (* Amiram Eldar, Sep 11 2021 *)

PARI

a(n) = n!*sum(i=0, n, (-1)^(n-i)*sum(j=0, n-i, i^j*stirling(n-i-j, j, 1)/(n-i-j)!)/i!);

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(x/(1-x)^x)))

Formula

a(n) = n! * Sum_{i=0..n} (-1)^(n-i) * ( Sum_{j=0..n-i} i^j * Stirling1(n-i-j,j)/(n-i-j)! )/i!.