cp's OEIS Frontend

A368359 Comma transform of Catalan numbers.

%I A368359 #18 Jan 04 2024 12:44:08
%S A368359 11,12,25,51,44,21,24,91,4,21,65,62,27,2,9,53,1,4,1,6,2,9,3,1,44,21,
%T A368359 26,42,1,83,41,95,82,8,43,21,24,41,6,2,1,3,1,5,2,8,3,1,5,21,67,62,21,
%U A368359 4,41,26,22,41,4,21,66,62,29,53,1,5,2,8,3,1,5,2,7,3,1,4,1,7,2,1,4,1,6,2,1,4,1,6,2,1,3,1,6,2,9,3,1,5,2,8
%N A368359 Comma transform of Catalan numbers.
%C A368359 See A367360 for further information.
%H A368359 Michael S. Branicky, <a href="/A368359/b368359.txt">Table of n, a(n) for n = 0..10000</a>
%p A368359 C:= proc(n) option remember; binomial(2*n, n)/(n+1) end:
%p A368359 a:= n-> parse(cat(""||(C(n))[-1], ""||(C(n+1))[1])):
%p A368359 seq(a(n), n=0..99);  # _Alois P. Heinz_, Jan 03 2024
%o A368359 (Python)
%o A368359 from math import comb
%o A368359 def A368359(n): return 10*(comb(n<<1,n)//(n+1)%10)+int(str(comb(n+1<<1,n+1)//(n+2))[0]) # _Chai Wah Wu_, Jan 03 2024
%o A368359 (Python)
%o A368359 from itertools import count, islice, pairwise
%o A368359 def S(): # generator of Catalan numbers as strings
%o A368359     C = 1
%o A368359     for n in count(0):
%o A368359         yield str(C)
%o A368359         C = C*(4*n+2)//(n+2)
%o A368359 def agen(): yield from (int(t[-1]+u[0]) for t, u in pairwise(S()))
%o A368359 print(list(islice(agen(), 100))) # _Michael S. Branicky_, Jan 04 2024
%Y A368359 Cf. A000108, A367360.
%K A368359 nonn,look,base
%O A368359 0,1
%A A368359 _N. J. A. Sloane_, Jan 02 2024