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A288326 Number of Dyck paths of semilength n such that each positive level has exactly ten peaks. 2
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 594, 10296, 84084, 378378, 1009008, 1633632, 1575288, 831402, 184756, 0, 121, 13794, 686070, 19744296, 375698466, 5114697588, 52484019588, 421146343332, 2715042399498, 14352204442576 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,22

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Wikipedia, Counting lattice paths

MAPLE

b:= proc(n, k, j) option remember;

     `if`(n=j, 1, add(b(n-j, k, i)*(binomial(i, k)

      *binomial(j-1, i-1-k)), i=1..min(j+k, n-j)))

    end:

a:= n-> `if`(n=0, 1, b(n, 10$2)):

seq(a(n), n=0..45);

MATHEMATICA

b[n_, k_, j_] := b[n, k, j] = If[n == j, 1, Sum[b[n - j, k, i]*(Binomial[i, k]*Binomial[j - 1, i - 1 - k]), {i, 1, Min[j + k, n - j]}]];

a[n_] := If[n == 0, 1, b[n, 10, 10]];

Table[a[n], {n, 0, 45}] (* Jean-Fran├žois Alcover, Jun 02 2018, from Maple *)

CROSSREFS

Column k=10 of A288318.

Cf. A000108.

Sequence in context: A185203 A265978 A263184 * A260583 A079915 A185656

Adjacent sequences:  A288323 A288324 A288325 * A288327 A288328 A288329

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jun 07 2017

STATUS

approved

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Last modified September 23 14:40 EDT 2021. Contains 347618 sequences. (Running on oeis4.)