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A023430 Generalized Catalan Numbers. 1

%I #16 Jul 20 2021 19:00:20

%S 1,1,1,1,1,1,1,1,2,4,7,11,17,27,44,72,118,194,320,528,871,1439,2385,

%T 3965,6605,11017,18399,30771,51538,86440,145165,244085,410890,692442,

%U 1168114,1972470,3333834,5639888,9549311,16181931,27442827,46575013

%N Generalized Catalan Numbers.

%F G.f. A(x) satisfies: A(x) = (1 + x^4 * A(x)^2) / (1 - x + x^4 + x^5 + x^6 + x^7). - _Ilya Gutkovskiy_, Jul 20 2021

%p A023430 := proc(n)

%p option remember;

%p if n = 0 then

%p 1;

%p else

%p procname(n-1)+add(procname(k)*procname(n-4-k),k=4..n-4) ;

%p end if;

%p end proc: # _R. J. Mathar_, May 01 2015

%t Clear[ a ]; a[ 0 ]=1; a[ n_Integer ] := a[ n ]=a[ n-1 ]+Sum[ a[ k ]*a[ n-4-k ], {k, 4, n-4} ];

%Y Cf. A000108, A001006, A004148, A006318.

%K nonn,easy

%O 0,9

%A _Olivier GĂ©rard_

%E More terms from _Sean A. Irvine_, Jun 04 2019

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Last modified March 29 11:14 EDT 2024. Contains 371278 sequences. (Running on oeis4.)