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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

Alois P. Heinz, Table of n, a(n) for n = 0..40

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

Adjacent sequences:  A289479 A289480 A289481 * A289483 A289484 A289485

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 06 2017

STATUS

approved

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Last modified February 29 07:39 EST 2020. Contains 332355 sequences. (Running on oeis4.)