A316186 Expansion of e.g.f. P(P(x)), where P(x) = Sum_{k>=1} prime(k)*x^k/k!.

4, 18, 104, 687, 5064, 40934, 358083, 3346832, 33123000, 345219919, 3777134694, 43291666298, 518855171115, 6491738816768, 84656365477452, 1148895613585775, 16201725990730392, 237030534528945348, 3591398122456079285, 56254812062478841340, 909319044063443870702

Offset

1,1

Comments

Self-composition of e.g.f. of A000040 (prime numbers).

Links

Table of n, a(n) for n=1..21.

N. J. A. Sloane, Transforms

Example

E.g.f.: A(x) = 4*x + 18*x^2/2! + 104*x^3/3! + 687*x^4/4! + 5064*x^5/5! + 40934*x^6/6! + ...

Mathematica

p[x_] := p[x] = Sum[Prime[k] x^k/k!, {k, 21}]; a[n_] := a[n] = SeriesCoefficient[p[p[x]], {x, 0, n}]; Table[n! a[n], {n, 21}]

Crossrefs

Cf. A000040, A014342, A014345, A030278.

Sequence in context: A335459 A159666 A349021 * A231274 A051827 A007711

Adjacent sequences: A316183 A316184 A316185 * A316187 A316188 A316189

Keyword

nonn

Author

Ilya Gutkovskiy, Jun 26 2018

Status

approved