A210431 Number of semistandard Young tableaux over all partitions of 9 with maximal element <= n.

0, 1, 30, 434, 3740, 22220, 100562, 370909, 1168008, 3245311, 8148590, 18821968, 40542228, 82300842, 158779362, 293092635, 520505744, 893364637, 1487517086, 2410539918, 3812130380, 5897064040, 8941168786, 13310814265, 19486468504, 28090928475, 39922889006

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 (10,-45,120,-210,252,-210,120,-45,10,-1).

Crossrefs

Row n=9 of A210391.

Programs

Maple

a:= n-> n*(10080+(40484+(31395+(8106+655*n^2)*n^2)*n^2)*n^2)/90720:
seq(a(n), n=0..40);

Formula

a(n) = n*(10080+(40484+(31395+(8106+655*n^2)*n^2)*n^2)*n^2)/90720.

G.f.: x*(x^8+20*x^7+179*x^6+630*x^5+960*x^4+630*x^3+179*x^2+20*x+1) / (x-1)^10.