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 A075196 Table T(n,k) by antidiagonals: T(n,k) = number of partitions of n balls of k colors. 12
 1, 2, 2, 3, 6, 3, 4, 12, 14, 5, 5, 20, 38, 33, 7, 6, 30, 80, 117, 70, 11, 7, 42, 145, 305, 330, 149, 15, 8, 56, 238, 660, 1072, 906, 298, 22, 9, 72, 364, 1260, 2777, 3622, 2367, 591, 30, 10, 90, 528, 2198, 6174, 11160, 11676, 6027, 1132, 42, 11, 110, 735, 3582, 12292, 28784, 42805, 36450, 14873, 2139, 56 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For k>=1, n->infinity is log(T(n,k)) ~ (1+1/k) * k^(1/(k+1)) * Zeta(k+1)^(1/(k+1)) * n^(k/(k+1)). - Vaclav Kotesovec, Mar 08 2015 LINKS Alois P. Heinz, Rows n = 1..141, flattened FORMULA T(n,k) = Sum_{i=0..k} C(k,i) * A255903(n,i). - Alois P. Heinz, Mar 10 2015 EXAMPLE 1,  2,   3,    4,    5, ... 2,  6,  12,   20,   30, ... 3, 14,  38,   80,  145, ... 5, 33, 117,  305,  660, ... 7, 70, 330, 1072, 2777, ... MAPLE with(numtheory): A:= proc(n, k) option remember; local d, j;       `if`(n=0, 1, add(add(d*binomial(d+k-1, k-1),        d=divisors(j)) *A(n-j, k), j=1..n)/n)     end: seq(seq(A(n, 1+d-n), n=1..d), d=1..12);  # Alois P. Heinz, Sep 26 2012 MATHEMATICA Transpose[Table[nn=6; p=Product[1/(1- x^i)^Binomial[i+n, n], {i, 1, nn}]; Drop[CoefficientList[Series[p, {x, 0, nn}], x], 1], {n, 0, nn}]]//Grid  (* Geoffrey Critzer, Sep 27 2012 *) CROSSREFS Columns 1-10: A000041, A005380, A217093, A255050, A255052, A270239, A270240, A270241, A270242, A270243. Rows 1-3: A000027, A002378, A162147. Main diagonal: A075197. Cf. A255903. Sequence in context: A183474 A294034 A210220 * A196912 A197079 A208340 Adjacent sequences:  A075193 A075194 A075195 * A075197 A075198 A075199 KEYWORD nonn,tabl AUTHOR Christian G. Bower, Sep 07 2002 STATUS approved

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Last modified August 8 05:50 EDT 2020. Contains 336290 sequences. (Running on oeis4.)