A210432 Number of semistandard Young tableaux over all partitions of 10 with maximal element <= n.

0, 1, 36, 630, 6512, 45628, 239316, 1007083, 3570240, 11042199, 30569012, 77221232, 180646896, 395884866, 820217412, 1618520277, 3060257024, 5572071725, 9810869508, 16763347626, 27879160048, 45246275592, 71818632820, 111707913791, 170553162816, 255984075075

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 (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Crossrefs

Row n=10 of A210391.

Programs

Maple

a:= n-> n^2* (126432+ (206020+ (101031+ (18930+ 1187*n^2) *n^2) *n^2) *n^2)/ 453600:
seq(a(n), n=0..40);

Formula

a(n) = n^2*(126432+(206020+(101031+(18930+1187*n^2)*n^2)*n^2)*n^2)/453600.

G.f.: -x*(x+1)*(x^8 +24*x^7 +265*x^6 +1132*x^5 +1904*x^4 +1132*x^3 +265*x^2 +24*x+1) / (x-1)^11.