A210429 Number of semistandard Young tableaux over all partitions of 7 with maximal element <= n.

0, 1, 20, 189, 1100, 4615, 15372, 43219, 106808, 238581, 491380, 946913, 1726308, 3002987, 5018092, 8098695, 12679024, 19324937, 28761876, 41906533, 59902460, 84159855, 116399756, 158702875, 213563304, 283947325, 373357556, 485902665, 626372884, 800321555

Offset

0,3

Links

Bruno Berselli, Table of n, a(n) for n = 0..1000

Wikipedia, Young tableau

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Formula

a(n) = n*(180+(637+(385+58*n^2)*n^2)*n^2)/1260.

G.f.: x*(x+1)^2*(x^4+10*x^3+36*x^2+10*x+1)/(x-1)^8.

Maple

a:= n-> n*(180+(637+(385+58*n^2)*n^2)*n^2)/1260:
seq(a(n), n=0..40);

Mathematica

CoefficientList[Series[x (x+1)^2(x^4+10x^3+36x^2+10x+1)/(x-1)^8, {x, 0, 40}], x] (* or *) LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {0, 1, 20, 189, 1100, 4615, 15372, 43219}, 40] (* Harvey P. Dale, Jan 29 2023 *)

Crossrefs

Row n=7 of A210391.

Sequence in context: A219581 A177073 A211153 * A367780 A047645 A010936

Adjacent sequences: A210426 A210427 A210428 * A210430 A210431 A210432

Keyword

nonn,easy

Author

Alois P. Heinz, Mar 21 2012

Status

approved