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%I #10 Aug 10 2021 11:06:59
%S 1,1,3,3,15,5,105,105,63,315,3465,495,6435,9009,15015,15015,255255,
%T 23205,37791,188955,101745,1119195,25741485,572033,42902475,79676025,
%U 42181425,42181425,155687805,40970475,1270084725,1270084725,665282475,173996955,6089893425,794333925
%N a(n) is the denominator of Catalan-Daehee number d(n).
%H Dae San Kim and Taekyun Kim, <a href="https://doi.org/10.1134/S1061920817040057">A new approach to Catalan numbers using differential equations</a>, Russ. J. Math. Phys. 24, 465-475 (2017).
%H Taekyun Kim and Dae San Kim, <a href="https://www.researchgate.net/publication/349589625_SOME_IDENTITIES_OF_CATALAN-DAEHEE_POLYNOMIALS_ARISING_FROM_UMBRAL_CALCULUS">Some identities of Catalan-Daehee polynomials arising from umbral calculus</a>, Appl. Comput. Math. 16 (2017), no. 2, 177-189.
%H Yuankui Ma, Taekyun Kim, Dae San Kim and Hyunseok Lee, <a href="https://arxiv.org/abs/2105.12013">Study on q-analogues of Catalan-Daehee numbers and polynomials</a>, arXiv:2105.12013 [math.NT], 2021.
%F G.f. of d(n): log(1 - 4*x)/(2*(sqrt(1 - 4*x) - 1)).
%F a(n) = denominator(d(n)), where d(n) = 4^n/(n + 1) - Sum_{m=0..n-1} 4^(n-m-1)*C(m)/(n - m) with d(0) = 1 and C(m) the m-th Catalan number.
%t nmax:=36; a[n_]:=Denominator[Coefficient[Series[Log[1-4x]/(2(Sqrt[1-4x]-1)),{x,0,nmax}],x,n]]; Array[a,nmax,0] (* or *)
%t a[n_]:=Denominator[If[n==0,1,4^n/(n+1)-Sum[4^(n-m-1)CatalanNumber[m]/(n-m),{m,0,n-1}]]]; Array[a,36,0]
%Y Cf. A000108, A000302, A014973 (denominators of Daehee numbers), A343206, A344849 (numerators).
%K nonn,frac
%O 0,3
%A _Stefano Spezia_, May 30 2021
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