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A140925
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Binomial(m+n-1,n)^2-binomial(m+n,n+1)*binomial(m+n-2,n-1) with m=12.
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6
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1, 66, 1716, 26026, 273273, 2186184, 14158144, 77364144, 367479684, 1551580888, 5924217936, 20734762776, 67255063876, 203982391536, 582806832960, 1578435172600, 4073755482225, 10064572367850, 23896002230100, 54709268263650, 121141951155225, 260114319363600
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OFFSET
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0,2
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COMMENTS
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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]
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REFERENCES
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S. Mukai, An Introduction to Invariants and Moduli, Cambridge, 2003; Prop. 8.4, case n=12. - N. J. A. Sloane, Aug 28 2010.
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LINKS
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Bruno Berselli, Table of n, a(n) for n = 0..1000
Index to sequences with linear recurrences with constant coefficients,
signature (21,-210,1330,-5985,20349,-54264,116280,-203490,293930,-352716,352716,-293930,203490,
-116280,54264,-20349,5985,-1330,210,-21,1).
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FORMULA
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(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]
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MATHEMATICA
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Table[Binomial[11 + n, n]^2 - Binomial[12 + n, n + 1] Binomial[10 + n, n - 1], {n, 0, 21}] (* Bruno Berselli, May 07 2012 *)
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PROG
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(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
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CROSSREFS
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Cf. A001263, A134291, A140934.
Sequence in context: A104673 A133318 A197645 * A017782 A035728 A114252
Adjacent sequences: A140922 A140923 A140924 * A140926 A140927 A140928
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KEYWORD
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nonn,easy
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AUTHOR
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R. H. Hardin, Jul 05 2008
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EXTENSIONS
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Edited by N. J. A. Sloane, Aug 28 2010.
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STATUS
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approved
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