A343263 a(0) = 1; a(n+1) = exp(-a(n)) * Sum_{k>=0} a(n)^k * k^n / k!.

1, 1, 1, 2, 22, 301554, 2493675105669492542968967478

Offset

0,4

Comments

The next term is too large to include.

Links

Table of n, a(n) for n=0..6.

Formula

a(0) = 1; a(n+1) = n! * [x^n] exp(a(n) * (exp(x) - 1)).

a(0) = 1; a(n+1) = Sum_{k=0..n} Stirling2(n,k) * a(n)^k.

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[StirlingS2[n - 1, k] a[n - 1]^k, {k, 0, n - 1}]; Table[a[n], {n, 0, 6}]
a[0] = 1; a[n_] := a[n] = BellB[n - 1, a[n - 1]]; Table[a[n], {n, 0, 6}]

Crossrefs

Cf. A000110, A003659, A067691, A110386, A189233, A242817, A292860, A294373.

Sequence in context: A246852 A060601 A053952 * A261198 A052077 A124604

Adjacent sequences: A343260 A343261 A343262 * A343264 A343265 A343266

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 09 2021

Status

approved