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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 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.)