A193365 - OEIS

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A193365

a(n) = A220371(n)/(4*A220371(n-1))

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

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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

Table of n, a(n) for n=1..34.

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)