OFFSET
0,3
COMMENTS
Unlike the nearly identical sequence A092918, this sequence does not count under a(1) the a single-vertex hypergraph with no edges.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..11
FORMULA
E.g.f.: 1 - x + log(Sum_{n >= 0} 2^(2^n-1) * x^n/n!).
Logarithmic transform of A003465.
EXAMPLE
The a(2) = 4 set-systems:
{{1, 2}}
{{1}, {1,2}}
{{2}, {1,2}}
{{1}, {2}, {1,2}}
MAPLE
b:= n-> add(binomial(n, k)*2^(2^(n-k)-1)*(-1)^k, k=0..n):
a:= proc(n) option remember; b(n)-`if`(n=0, 0, add(
k*binomial(n, k)*b(n-k)*a(k), k=1..n-1)/n)
end:
seq(a(n), n=0..8); # Alois P. Heinz, Jan 30 2019
MATHEMATICA
nn=8;
ser=Sum[2^(2^n-1)*x^n/n!, {n, 0, nn}];
Table[SeriesCoefficient[1-x+Log[ser], {x, 0, n}]*n!, {n, 0, nn}]
PROG
(Magma)
m:=12;
f:= func< x | 1-x + Log( (&+[2^(2^n-1)*x^n/Factorial(n): n in [0..m+2]]) ) >;
R<x>:=PowerSeriesRing(Rationals(), m);
Coefficients(R!(Laplace( f(x) ))); // G. C. Greubel, Oct 04 2022
(SageMath)
m=12;
def f(x): return 1-x + log(sum(2^(2^n-1)*x^n/factorial(n) for n in range(m+2)))
def A_list(prec):
P.<x> = PowerSeriesRing(QQ, prec)
return P( f(x) ).egf_to_ogf().list()
A_list(m) # G. C. Greubel, Oct 04 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 30 2019
STATUS
approved