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A193365 a(n) = A220371(n)/(4*A220371(n-1)) 3
15, 126, 143, 1020, 399, 1150, 783, 8184, 1295, 3198, 1935, 9212, 2703, 6270, 3599, 65520, 4623, 10366, 5775, 25596, 7055, 15486, 8463, 73720, 9999, 21630, 11663, 50172, 13455, 28798, 15375, 524256, 17423, 36990 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
This sequence is, via A220371, related to A220002, which is related to the Catalan numbers.
Information about the peculiar structure of the a(n) can be found in A220466.
LINKS
FORMULA
a(n) = A220371(n)/(4*A220371(n-1))
a(2^p*(2*n-1)) = 2^p*(2^(2*p+4)*(2*n-1)^2-1), p >= 0.
MAPLE
nmax:= 34: for p from 0 to ceil(simplify(log[2](nmax))) do for n from 1 to ceil(nmax/(p+2)) do a(2^p*(2*n-1)) := 2^p*(2^(2*p+4)*(2*n-1)^2-1) od: od: seq(a(n), n=1..nmax);
MATHEMATICA
b[n_] := b[n] = 2^(2n) Product[2i+1, {i, 1, 2n}] GCD[n!, 2^n];
a[n_] := b[n]/(4 b[n-1]);
Array[a, 34] (* Jean-François Alcover, Jun 26 2019 *)
PROG
(Sage)
def A193365_list(len):
a = {}; z = 1; s = 0; p = 1
while s < len:
i = s; z += z
while i < len:
a[i] = p*((4*i+4)^2-1)
i += z
s += s + 1; p += p
return [a[i] for i in range(len)]
A193365_list(30) # Peter Luschny, Dec 22 2012
CROSSREFS
Sequence in context: A034271 A171220 A071080 * A069975 A027779 A337958
KEYWORD
nonn,easy
AUTHOR
Johannes W. Meijer, Dec 21 2012
STATUS
approved

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Last modified March 29 05:48 EDT 2024. Contains 371265 sequences. (Running on oeis4.)