A368359 Comma transform of Catalan numbers.

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, 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, 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

Offset: 0

Author

N. J. A. Sloane, Jan 02 2024

Keywords

• nonn
• look
• base

Comments

See A367360 for further information.

Links

• Michael S. Branicky, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000108, A367360.

Programs

Maple

C:= proc(n) option remember; binomial(2*n, n)/(n+1) end:
a:= n-> parse(cat(""||(C(n))[-1], ""||(C(n+1))[1])):
seq(a(n), n=0..99);  # Alois P. Heinz, Jan 03 2024

Python

from math import comb
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

Python

from itertools import count, islice, pairwise
def S(): # generator of Catalan numbers as strings
    C = 1
    for n in count(0):
        yield str(C)
        C = C*(4*n+2)//(n+2)
def agen(): yield from (int(t[-1]+u[0]) for t, u in pairwise(S()))
print(list(islice(agen(), 100))) # Michael S. Branicky, Jan 04 2024