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A354540 Number of decorated Dyck paths of length n ending at arbitrary levels. 0
1, 1, 2, 3, 7, 11, 26, 43, 102, 175, 416, 733, 1745, 3137, 7476, 13651, 32559, 60199, 143672, 268369, 640823, 1207277, 2884008, 5472821, 13078414, 24973213, 59696622, 114609547, 274037261, 528622499, 1264251474, 2449053107 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..31.

H. Prodinger, Partial skew Dyck paths -- a kernel method, arXiv:2108.09785 [math.CO], 2021-2022, chapter 3.

FORMULA

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)) .

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.

MAPLE

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)) ;

taylor(%, z=0, 30) ;

gfun[seriestolist](%) ;

CROSSREFS

Sequence in context: A294451 A005246 A116406 * A112843 A036651 A049454

Adjacent sequences: A354537 A354538 A354539 * A354541 A354542 A354543

KEYWORD

nonn

AUTHOR

R. J. Mathar, Aug 17 2022

STATUS

approved

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Last modified April 1 22:06 EDT 2023. Contains 361713 sequences. (Running on oeis4.)