A347006 E.g.f.: Product_{k>=1} (1 + exp(x) * x^k / k!).

1, 1, 3, 10, 43, 206, 1044, 5909, 38371, 272314, 1995208, 14869889, 115433344, 965259881, 8773348601, 84608514095, 837220780691, 8334354200226, 83498917650084, 855936118936073, 9180736840445788, 104439240481045949, 1253608634906635901

Offset

0,3

Links

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

Formula

E.g.f.: exp( Sum_{k>=1} ( Sum_{d|k} (-1)^(d+1) * exp(d*x) / (d * ((k/d)!)^d) ) * x^k ).

E.g.f.: Product_{k>=1} (1 + Sum_{j>=k} binomial(j,k) * x^j / j!).

Mathematica

nmax = 22; CoefficientList[Series[Product[(1 + Exp[x] x^k/k!), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!

Crossrefs

Cf. A007837, A265952, A305547, A347005.

Sequence in context: A151084 A151085 A082936 * A205487 A323667 A030935

Adjacent sequences: A347003 A347004 A347005 * A347007 A347008 A347009

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 10 2021

Status

approved