OFFSET
0,3
COMMENTS
Exponential transform of A008578.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..534
N. J. A. Sloane, Transforms
FORMULA
E.g.f.: exp(Sum_{k>=1} A008578(k)*x^k/k!).
EXAMPLE
E.g.f.: A(x) = 1 + x/1! + 3*x^2/2! + 10*x^3/3! + 42*x^4/4! + 203*x^5/5! + 1119*x^6/6! + 6839*x^7/7! + ..
MAPLE
a:= proc(n) option remember; (p-> `if`(n=0, 1, add(a(n-j)*p(j)*
binomial(n-1, j-1), j=1..n)))(t-> `if`(t=1, 1, ithprime(t-1)))
end:
seq(a(n), n=0..25); # Alois P. Heinz, Mar 10 2018
MATHEMATICA
nmax = 23; CoefficientList[Series[Exp[x + Sum[Prime[k - 1] x^k/k!, {k, 2, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
p[1] = 1; p[n_] := p[n] = Prime[n - 1]; a[n_] := a[n] = Sum[p[k] Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 23}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 10 2018
STATUS
approved