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A289482 Number of Dyck paths of semilength n^2 and height n. 2
1, 1, 7, 1341, 5828185, 517500496981, 877820839402932499, 27202373147496127842409429, 14934414860406931133627906259665137, 142143740345412121643458345045577780672138977, 23087568034858117342849941754170955046637454778184629205 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) = A289481(n,n).
a(n) ~ c * 2^(2*n^2) / n^4, where c = 0.034180619793706218467525729844898502557235639065782754227258170112282483988... - Vaclav Kotesovec, Jul 14 2017
MAPLE
b:= proc(x, y, k) option remember;
`if`(x=0, 1, `if`(y>0, b(x-1, y-1, k), 0)+
`if`(y < min(x-1, k), b(x-1, y+1, k), 0))
end:
a:= n-> `if`(n=0, 1, b(2*n^2, 0, n)-b(2*n^2, 0, n-1)):
seq(a(n), n=0..12);
MATHEMATICA
b[x_, y_, k_]:=b[x, y, k]=If[x==0, 1, If[y>0, b[x - 1, y - 1, k], 0] + If[y<Min[x - 1, k], b[x - 1, y + 1, k], 0]]; a[n_]:=a[n]=If[n==0, 1, b[2n^2, 0, n] - b[2n^2, 0, n - 1]]; Table[a[n], {n, 0, 12}] (* Indranil Ghosh, Jul 08 2017 *)
CROSSREFS
Main diagonal of A289481.
Sequence in context: A119181 A152518 A210396 * A214010 A145451 A144676
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 06 2017
STATUS
approved

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Last modified June 15 11:51 EDT 2024. Contains 373407 sequences. (Running on oeis4.)