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A210430
Number of semistandard Young tableaux over all partitions of 8 with maximal element <= n.
2
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
0,3
LINKS
Wikipedia, Young tableau
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
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.
MAPLE
a:= n-> n^2*(n^2+3)*(1124+(1205+191*n^2)*n^2)/10080:
seq(a(n), n=0..40);
CROSSREFS
Row n=8 of A210391.
Sequence in context: A029987 A017582 A335598 * A158990 A079873 A078488
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Mar 21 2012
STATUS
approved