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A354540 Number of decorated Dyck paths of length n ending at arbitrary levels. 0

%I #10 Aug 17 2022 11:49:55

%S 1,1,2,3,7,11,26,43,102,175,416,733,1745,3137,7476,13651,32559,60199,

%T 143672,268369,640823,1207277,2884008,5472821,13078414,24973213,

%U 59696622,114609547,274037261,528622499,1264251474,2449053107

%N Number of decorated Dyck paths of length n ending at arbitrary levels.

%H H. Prodinger, <a href="https://arxiv.org/abs/2108.09785">Partial skew Dyck paths -- a kernel method</a>, arXiv:2108.09785 [math.CO], 2021-2022, chapter 3.

%F G.f.: -((z+1)*(z^2+3*z-2)+(z+2)*sqrt(1-6*z^2+5*z^4))/(2*z*(z^2+2*z-1)) .

%F D-finite with recurrence 2*(n+1)*a(n) +(-3*n-5)*a(n-1) +8*(-2*n+3)*a(n-2) +(17*n-23)*a(n-3) +2*(17*n-61)*a(n-4) +(-9*n+41)*a(n-5) +20*(-n+6)*a(n-6) +5*(-n+7)*a(n-7)=0.

%p g := -((z+1)*(z^2+3*z-2)+(z+2)*sqrt(1-6*z^2+5*z^4))/(2*z*(z^2+2*z-1)) ;

%p taylor(%,z=0,30) ;

%p gfun[seriestolist](%) ;

%K nonn

%O 0,3

%A _R. J. Mathar_, Aug 17 2022

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)