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| A210485
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Number T(n,k) of parts in all partitions of n in which no part occurs more than k times; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
(history;
published version)
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#30 by Alois P. Heinz at Sun Jul 16 15:36:39 EDT 2023
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#29 by Alois P. Heinz at Sat Jul 15 19:55:17 EDT 2023
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#28 by Alois P. Heinz at Sat Jul 15 17:28:20 EDT 2023
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| EXAMPLE
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| STATUS
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approved
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#27 by Vaclav Kotesovec at Thu Oct 18 10:20:26 EDT 2018
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#26 by Vaclav Kotesovec at Thu Oct 18 09:37:31 EDT 2018
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| COMMENTS
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For fixed k > 0, T(n,k) ~ 3^(1/4) * log(k+1) * exp(Pi*sqrt(2*k*n/(3*(k+1)))) / (Pi * (8*k*(k+1)*n)^(1/4)). - Vaclav Kotesovec, Oct 18 2018
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#25 by Alois P. Heinz at Wed Oct 17 14:22:37 EDT 2018
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#24 by Alois P. Heinz at Wed Oct 17 14:22:35 EDT 2018
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#23 by Alois P. Heinz at Wed Oct 17 11:39:06 EDT 2018
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#22 by Alois P. Heinz at Wed Oct 17 10:23:25 EDT 2018
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| CROSSREFS
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Columns k=0-310 give: A000004, A015723, A185350, A117148, A320607, A320608, A320609, A320610, A320611, A320612, A320613.
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#21 by Alois P. Heinz at Thu Oct 11 15:24:16 EDT 2018
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DiagonalMain diagonal gives: A006128.
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