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 A354539 Number of decorated Dyck paths of length n without peaks at level 1 ending at arbitrary levels. 0
 1, 1, 1, 2, 5, 8, 18, 31, 71, 126, 290, 527, 1218, 2253, 5223, 9796, 22763, 43170, 100502, 192347, 448476, 864887, 2019121, 3919162, 9159252, 17877619, 41819003, 82021628, 192015633 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Table of n, a(n) for n=0..28. H. Prodinger, Skew Dyck paths having no peaks at level 1, JIS 25 (2022) # 22.1.16, section 2.3. FORMULA G.f.: (-2*z^5-3*z^4+z^3-5*z^2-3*z+4-(z^2+3*z+4)*sqrt(1-6*z^2+5*z^4))/2/z/(3+z^2)/(z^2+2*z-1) . D-finite with recurrence 12*(n+1)*a(n) +3*(-5*n-11)*a(n-1) +5*(-19*n+29)*a(n-2) +14*(5*n-4)*a(n-3) +2*(93*n-356)*a(n-4) +2*(20*n-81)*a(n-5) +2*(-22*n+217)*a(n-6) +2*(-35*n+268)*a(n-7) +2*(-27*n+182)*a(n-8) +5*(-5*n+39)*a(n-9) +5*(-n+9)*a(n-10)=0. MAPLE g := (-2*z^5-3*z^4+z^3-5*z^2-3*z+4-(z^2+3*z+4)*sqrt(1-6*z^2+5*z^4))/2/z/(3+z^2)/(z^2+2*z-1) ; taylor(%, z=0, 30) ; gfun[seriestolist](%) ; CROSSREFS Cf. A128723 (ending at level 0). Sequence in context: A063675 A000943 A304966 * A152006 A271619 A197211 Adjacent sequences: A354536 A354537 A354538 * A354540 A354541 A354542 KEYWORD nonn AUTHOR R. J. Mathar, Aug 17 2022 STATUS approved

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Last modified December 9 07:37 EST 2023. Contains 367689 sequences. (Running on oeis4.)