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

Author

Alois P. Heinz, Mar 21 2012

Keywords

• nonn
• easy

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).

Crossrefs

Row n=7 of A210391.

Programs

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 *)

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.