OFFSET
0,4
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..11
FORMULA
Inverse binomial transform of A016031 shifted once to the left.
EXAMPLE
The a(3) = 12 set-systems:
{{1,2,3}}
{{1,2}, {1,3}}
{{1,2}, {2,3}}
{{1,3}, {2,3}}
{{1,2}, {1,2,3}}
{{1,3}, {1,2,3}}
{{2,3}, {1,2,3}}
{{1,2}, {1,3}, {2,3}}
{{1,2}, {1,3}, {1,2,3}}
{{1,2}, {2,3}, {1,2,3}}
{{1,3}, {2,3}, {1,2,3}}
{{1,2}, {1,3}, {2,3}, {1,2,3}}
MAPLE
a:= n-> add(2^(2^(n-j)-n+j-1)*binomial(n, j)*(-1)^j, j=0..n):
seq(a(n), n=0..8); # Alois P. Heinz, Jan 30 2019
MATHEMATICA
Table[Sum[(-1)^(n-k)*Binomial[n, k]*2^(2^k-k-1), {k, 0, n}], {n, 0, 8}]
PROG
(Magma)
[(&+[(-1)^(n-j)*Binomial(n, j)*2^(2^j -j-1): j in [0..n]]): n in [0..12]]; // G. C. Greubel, Oct 05 2022
(SageMath)
def A323816(n): return sum((-1)^j*binomial(n, j)*2^(2^(n-j) -n+j-1) for j in range(n+1))
[A323816(n) for n in range(12)] # G. C. Greubel, Oct 05 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 30 2019
STATUS
approved