A215544 Number of standard Young tableaux of shape [4n,4].

0, 14, 275, 1260, 3705, 8602, 17199, 31000, 51765, 81510, 122507, 177284, 248625, 339570, 453415, 593712, 764269, 969150, 1212675, 1499420, 1834217, 2222154, 2668575, 3179080, 3759525, 4416022, 5154939, 5982900, 6906785, 7933730, 9071127, 10326624, 11708125

Offset

0,2

Comments

Also the number of binary words with 4n 1's and 4 0's such that for every prefix the number of 1's is >= the number of 0's. The a(1) = 14 words are: 10101010, 10101100, 10110010, 10110100, 10111000, 11001010, 11001100, 11010010, 11010100, 11011000, 11100010, 11100100, 11101000, 11110000.

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 (5,-10,10,-5,1).

Formula

G.f.: (3*x^4-15*x^3-25*x^2-205*x-14)*x/(x-1)^5.

a(n) = (4*n-3)*(4*n+3)*(2*n+1)*(n+1)/3 for n>0, a(0) = 0.

Maple

a:= n-> max(0, (4*n+3)*(2*n+1)*(4*n-3)*(n+1)/3):
seq(a(n), n=0..40);

Mathematica

LinearRecurrence[{5, -10, 10, -5, 1}, {0, 14, 275, 1260, 3705, 8602}, 40] (* Harvey P. Dale, Jan 25 2024 *)

Prog

(PARI) a(n)=max((4*n-3)*(4*n+3)*(2*n+1)*(n+1)/3, 0) \\ Charles R Greathouse IV, Oct 21 2022

Crossrefs

Row n=4 of A214776.

Sequence in context: A048668 A001820 A211900 * A205353 A279113 A291099

Adjacent sequences: A215541 A215542 A215543 * A215545 A215546 A215547

Keyword

nonn,easy

Author

Alois P. Heinz, Aug 15 2012

Status

approved