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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

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-Fran├žois 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

Cf. A220466

Sequence in context: A034271 A171220 A071080 * A069975 A027779 A073509

Adjacent sequences:  A193362 A193363 A193364 * A193366 A193367 A193368

KEYWORD

nonn,easy

AUTHOR

Johannes W. Meijer, Dec 21 2012

STATUS

approved

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Last modified January 26 05:10 EST 2020. Contains 331273 sequences. (Running on oeis4.)