|
|
A370070
|
|
a(n) = Sum_{i=0..n-1} binomial(2^i+2^(n-i-1)-2,2^i-1).
|
|
1
|
|
|
0, 1, 2, 4, 10, 38, 274, 5130, 353186, 180449810, 1025875786562, 474164444389402658, 13339869168335987186843266, 6036430661900479858398240235709517890, 3241401154265052413102761158540183436937430482058498
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
If n is odd, a(n) = binomial(2*(2^((n-1)/2)-1),2^((n-1)/2)-1) + 2*Sum_{i=0..(n-3)/2)} binomial(2^i+2^(n-i-1)-2,2^i-1).
If n is even, a(n) = 2*Sum_{i=0..n/2-1} binomial(2^i+2^(n-i-1)-2,2^i-1).
log(a(n)) ~ c * 2^(n/2), where c = 3*log(3)/2 - log(2) if n is even and c = sqrt(2)*log(2) if n is odd. - Vaclav Kotesovec, Feb 10 2024
|
|
MATHEMATICA
|
Table[Sum[Binomial[2^i+2^(n-i-1)-2, 2^i-1], {i, 0, n-1}], {n, 0, 14}] (* James C. McMahon, Feb 08 2024 *)
|
|
PROG
|
(Python)
from math import comb
def A370070(n): return (sum(comb((1<<i)+(1<<n-i-1)-2, (1<<i)-1) for i in range(n>>1))<<1) + (comb(((1<<(n>>1))-1)<<1, (1<<(n>>1))-1) if n&1 else 0)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|