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A024487
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a(n) = (1/(4n+2))*M(3n; n,n,n).
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2
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1, 9, 120, 1925, 34398, 659736, 13302432, 278397405, 5996669250, 132166590270, 2967978162240, 67694635250424, 1564409223571600, 36561597688116000, 862822254602816640, 20535537339485077005, 492426552811873991850, 11886753074132473787250, 288645723487776840570000
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OFFSET
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1,2
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COMMENTS
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Number of standard Young tableaux of shape (n,n,{1}^n). - Alois P. Heinz, Apr 05 2013
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LINKS
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FORMULA
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D-finite with recurrence: n^2*(2*n+1)*a(n) -3*(3*n-1)*(2*n-1)*(3*n-2)*a(n-1)=0. - R. J. Mathar, Apr 27 2020
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EXAMPLE
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G.f. = x + 9*x^2 + 120*x^3 + 1925*x^4 + 34398*x^5 + 659736*x^6 + ...
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MAPLE
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with(combinat):
a:= n-> multinomial(3*n, n$3)/(4*n+2):
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MATHEMATICA
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a[ n_] := If[ n < 1, 0, (3 n)! / (n!^3 (4 n + 2))]; (* Michael Somos, Oct 25 2014 *)
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PROG
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(PARI) {a(n) = if( n<1, 0, (3*n)! / (n!^3 * (4*n + 2)))}; /* Michael Somos, Oct 25 2014 */
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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