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 A172685 Number of 4*n X 3*n 0..2 arrays with row sums 3 and column sums 4. 1
 175, 20982583300, 853588467101915622000, 1760753561430175391642594031000000, 70118545603035216189674302236706595177583000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS R. H. Hardin, Table of n, a(n) for n = 1..24 FORMULA a(n) = 24^(-3n)*(3n)!(4n)! Sum_{i=0..3n} Sum_{j=0..3n-i} Sum_{k=0..min(n+i, 3n-i-j)} 6^j*3^k*(-16)^(3n-i-j-k)*(3i+j+3n-k)!/(i!j!k!(3n-i-j-k)!(n-k+i)!6^(n-k+i)). - Shanzhen Gao, Feb 24 2010 a(n) ~ sqrt(Pi) * 2^(11*n + 3/2) * 3^(5*n + 1/2) * n^(12*n + 1/2) / exp(12*n-3). - Vaclav Kotesovec, Oct 22 2023 MATHEMATICA Table[24^(-3*n)*(3*n)!*(4*n)! * Sum[Sum[Sum[6^j*3^k*(-16)^(3*n-i-j-k)*(3*i+j+3*n-k)! / (i!*j!*k!*(3*n-i-j-k)!*(n-k+i)!*6^(n-k+i)), {k, 0, Min[n+i, 3*n-i-j]}], {j, 0, 3*n-i}], {i, 0, 3*n}], {n, 1, 12}] (* Vaclav Kotesovec, Oct 22 2023 *) PROG (PARI) a(n) = 24^(-3*n)*(3*n)!*(4*n)!*sum(i=0, 3*n, sum(j=0, 3*n-i, sum(k=0, min(n+i, 3*n-i-j), 6^j*3^k*(-16)^(3*n-i-j-k)*(3*i+j+3*n-k)!/(i!*j!*k!*(3*n-i-j-k)!*(n-k+i)!*6^(n-k+i))))); \\ Michel Marcus, Jan 17 2018 CROSSREFS Sequence in context: A268872 A104651 A212946 * A344280 A266058 A261678 Adjacent sequences: A172682 A172683 A172684 * A172686 A172687 A172688 KEYWORD nonn AUTHOR R. H. Hardin, Feb 06 2010 STATUS approved

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Last modified April 19 10:31 EDT 2024. Contains 371791 sequences. (Running on oeis4.)