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A023423
Generalized Catalan Numbers.
5
1, 1, 1, 1, 1, 1, 1, 2, 4, 8, 16, 32, 64, 128, 257, 517, 1042, 2104, 4256, 8624, 17504, 35585, 72455, 147746, 301706, 616948, 1263240, 2589840, 5316033, 10924681, 22475831, 46290195
OFFSET
0,8
LINKS
FORMULA
G.f. A(x) satisfies: A(x) = (1 + x^2 * A(x)^2) / (1 - x + x^2 + x^3 + x^4 + x^5 + x^6). - Ilya Gutkovskiy, Jul 20 2021
MAPLE
A023423 := proc(n)
option remember;
if n <= 6 then
1;
else
procname(n-1)+add(procname(k)*procname(n-2-k), k=5..n-2) ;
end if;
end proc: # R. J. Mathar, Oct 10 2014
MATHEMATICA
a[0]=1; a[n_]:= a[n]=a[n-1] + Sum[a[k]*a[n-2-k], {k, 5, n-2}]; Table[a[n], {n, 0, 30}] (* modified by G. C. Greubel, Jan 01 2018 *)
PROG
(PARI) {a(n) = if(n==0, 1, a(n-1) + sum(k=5, n-2, a(k)*a(n-k-2)))};
for(n=0, 30, print1(a(n), ", ")) \\ G. C. Greubel, Jan 01 2018
CROSSREFS
Sixth row of A064645.
Sequence in context: A275063 A186026 A367653 * A210544 A180210 A274861
KEYWORD
nonn,easy
STATUS
approved