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 A140925 Binomial(m+n-1,n)^2-binomial(m+n,n+1)*binomial(m+n-2,n-1) with m=12. 6
 1, 66, 1716, 26026, 273273, 2186184, 14158144, 77364144, 367479684, 1551580888, 5924217936, 20734762776, 67255063876, 203982391536, 582806832960, 1578435172600, 4073755482225, 10064572367850, 23896002230100, 54709268263650, 121141951155225, 260114319363600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Number of 2 X 10 matrices with elements in 0..n with each row and each column in nondecreasing order. 2,10,n can be permuted, see formula. 11-th column (and diagonal) of the triangle A001263. [Bruno Berselli, May 07 2012] REFERENCES S. Mukai, An Introduction to Invariants and Moduli, Cambridge, 2003; Prop. 8.4, case n=12. - N. J. A. Sloane, Aug 28 2010. LINKS Bruno Berselli, Table of n, a(n) for n = 0..1000 signature (21,-210,1330,-5985,20349,-54264,116280,-203490,293930,-352716,352716,-293930,203490, -116280,54264,-20349,5985,-1330,210,-21,1). FORMULA (Empirical) set p,q,r to n,10,2 (in any order) in s=p+q+r-1; a(n) = product {i in 0..r-1} (binomial(s,p+i)*i!/(s-i)^(r-i-1)) G.f.: (1+x)*(1+44*x+496*x^2+2024*x^3+3268*x^4+2024*x^5+496*x^6+44*x^7+x^8)/(1-x)^21. [Bruno Berselli, May 07 2012] a(n) = ((n+11)/(11*n+11))*binomial(n+10,10)^2. [Bruno Berselli, May 07 2012] MATHEMATICA Table[Binomial[11 + n, n]^2 - Binomial[12 + n, n + 1] Binomial[10 + n, n - 1], {n, 0, 21}] (* Bruno Berselli, May 07 2012 *) PROG (Maxima) makelist(coeff(taylor((1+x)*(1+44*x+496*x^2+2024*x^3+3268*x^4+2024*x^5+496*x^6+44*x^7+x^8)/(1-x)^21, x, 0, n), x, n), n, 0, 21); [Bruno Berselli, May 07 2012] (MAGMA) [((n+11)/(11*n+11))*Binomial(n+10, 10)^2: n in [0..21]]; // Bruno Berselli, May 07 2012 CROSSREFS Cf. A001263, A134291, A140934. Sequence in context: A104673 A133318 A197645 * A017782 A035728 A114252 Adjacent sequences:  A140922 A140923 A140924 * A140926 A140927 A140928 KEYWORD nonn,easy AUTHOR R. H. Hardin, Jul 05 2008 EXTENSIONS Edited by N. J. A. Sloane, Aug 28 2010. STATUS approved

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