A215546 Number of standard Young tableaux of shape [6n,6].

0, 132, 9996, 92092, 451269, 1570800, 4395118, 10559208, 22664655, 44602348, 81921840, 142247364, 235740505, 375609528, 578665362, 865924240, 1263256995, 1802085012, 2520122836, 3462167436, 4680934125, 6237939136, 8204428854, 10662355704, 13705400695

Offset

0,2

Comments

Also the number of binary words with 6n 1's and 6 0's such that for every prefix the number of 1's is >= the number of 0's.

Links

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

Wikipedia, Young tableau.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

G.f.: (5*x^6-35*x^5-609*x^4-11921*x^3-24892*x^2-9072*x-132)*x/(x-1)^7.

a(n) = (6*n-5)*(6*n+5)*(3*n+2)*(2*n+1)*(3*n+1)*(n+1)/10 for n>0, a(0) = 0.

Sum_{n>=1} 1/a(n) = 76/385 - 1559*Pi/(924*sqrt(3)) + 2080*log(2)/231 - 135*log(3)/44. - Amiram Eldar, Aug 29 2025

Maple

a:= n-> max(0, (6*n-5)*(6*n+5)*(3*n+2)*(2*n+1)*(3*n+1)*(n+1)/10):
seq(a(n), n=0..40);

Prog

(PARI) a(n)=if(n, (648*n^6-585*n^3-928*n^2-375*n)/10+162*n^5+99*n^4-5, 0) \\ Charles R Greathouse IV, May 30 2026

Crossrefs

Row n=6 of A214776.

Sequence in context: A184893 A035818 A258394 * A269042 A216787 A239817

Adjacent sequences: A215543 A215544 A215545 * A215547 A215548 A215549

Keyword

nonn,easy,changed

Author

Alois P. Heinz, Aug 16 2012

Status

approved