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A288323 Number of Dyck paths of semilength n such that each positive level has exactly seven peaks. 2
1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 8, 216, 1800, 6600, 11880, 10296, 3432, 0, 64, 3744, 96768, 1454160, 14460480, 102586176, 544817856, 2237725512, 7268659712, 18954982080, 40057015680, 68941928016, 97350892224, 122456030112, 244967552640 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,16

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, 7$2)):

seq(a(n), n=0..40);

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, 7, 7]];

Table[a[n], {n, 0, 40}] (* Jean-Fran├žois Alcover, Jun 02 2018, from Maple *)

CROSSREFS

Column k=7 of A288318.

Cf. A000108.

Sequence in context: A334582 A195506 A069045 * A264056 A271400 A123057

Adjacent sequences:  A288320 A288321 A288322 * A288324 A288325 A288326

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jun 07 2017

STATUS

approved

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Last modified July 24 11:17 EDT 2021. Contains 346273 sequences. (Running on oeis4.)