A210430 Number of semistandard Young tableaux over all partitions of 8 with maximal element <= n.

0, 1, 25, 294, 2090, 10460, 40677, 131131, 366088, 912519, 2075965, 4381168, 8683962, 16321682, 29310113, 50595765, 84373024, 136476493, 214859601, 330171322, 496443610, 731902920, 1059919949, 1510112495, 2119617096, 2934545875, 4011645781, 5420178180

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 (9,-36,84,-126,126,-84,36,-9,1).

Crossrefs

Row n=8 of A210391.

Programs

Maple

a:= n-> n^2*(n^2+3)*(1124+(1205+191*n^2)*n^2)/10080:
seq(a(n), n=0..40);

Formula

a(n) = n^2*(n^2+3)*(1124+(1205+191*n^2)*n^2)/10080.

G.f.: -x*(x+1)*(x^6+15*x^5+90*x^4+170*x^3+90*x^2+15*x+1)/(x-1)^9.