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

Offset: 1

Author

Johannes W. Meijer, Dec 21 2012

Keywords

• nonn
• easy

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.

Crossrefs

Cf. A220466

Programs

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 *)

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

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.