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A105124
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Three-dimensional small Schroeder numbers.
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1
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1, 1, 11, 197, 4593, 126289, 3888343, 130016393, 4629617873, 173225211953, 6746427428131, 271578345652109, 11240106619304609, 476332107976984545, 20601333127791572143, 906951532759564554769, 40554743852511698293601
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OFFSET
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0,3
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COMMENTS
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a(n) = number of increasing tableaux of shape (n,n,n). An increasing tableau is a semistandard tableau with strictly increasing rows and columns, and set of entries an initial segment of the positive integers. - Oliver Pechenik, May 03 2014
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LINKS
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FORMULA
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a(0)=1, a(n) = Sum_{k=0..2*n-2} 2^k*Sum_{j=0..k} 2*(-1)^(k-j)*C(3*n+1, k-j)*C(n+j, n)*C(n+j+1, n)*C(n+j+2, n)/(n+1)^2/(n+2) (Sulanke). (End)
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PROG
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(PARI) {alias(C, binomial); a(n)=if(n==0, 1, sum(k=0, 2*n-2, 2^k*sum(j=0, k, 2*(-1)^(k-j)*C(3*n+1, k-j)*C(n+j, n)*C(n+j+1, n)*C(n+j+2, n)/(n+1)^2/(n+2))))} \\ Hanna
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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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