A372623 Expansion of e.g.f. exp( exp(x) * (1 + x^2 / 2) - 1 ).

1, 1, 3, 11, 48, 247, 1448, 9445, 67651, 526704, 4418875, 39670270, 378931567, 3832882393, 40886570975, 458341921775, 5382862509572, 66050096110691, 844741961321026, 11236481306649167, 155150031880549077, 2219877203279634396, 32860282502526114729

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * A000124(k-1) * a(n-k).

Mathematica

nmax = 22; CoefficientList[Series[Exp[Exp[x] (1 + x^2/2) - 1], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] (k (k - 1)/2 + 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 22}]

Crossrefs

Cf. A000124, A209801, A279361.

Sequence in context: A317170 A127087 A113060 * A186374 A187249 A105151

Adjacent sequences: A372620 A372621 A372622 * A372624 A372625 A372626

Keyword

nonn

Author

Ilya Gutkovskiy, May 07 2024

Status

approved