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 A060244 Triangle a(n,k) of bipartite partitions of n objects into parts >1, k of which are black. 8
 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 2, 2, 2, 3, 4, 4, 3, 2, 4, 5, 8, 8, 8, 5, 4, 4, 7, 11, 13, 13, 11, 7, 4, 7, 11, 19, 22, 26, 22, 19, 11, 7, 8, 15, 26, 35, 40, 40, 35, 26, 15, 8, 12, 22, 41, 54, 69, 70, 69, 54, 41, 22, 12, 14, 30, 56, 81, 104, 116, 116, 104, 81, 56, 30, 14, 21, 42 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,11 REFERENCES P. A. MacMahon, Memoir on symmetric functions of the roots of systems of equations, Phil. Trans. Royal Soc. London, 181 (1890), 481-536; Coll. Papers II, 32-87. LINKS FORMULA G.f.: Product_{ i=2..infinity, j=0..i} 1/(1-x^(i-j)*y^j). EXAMPLE Series ends ... + 2*x^5 + 3*x^4*y + 4*x^3*y^2 + 4*x^2*y^3 + 3*x*y^4 + 2*y^5 + 2*x^4 + 2*x^3*y + 3*x^2*y^2 + 2*x*y^3 + 2*y^4 + x^3 + x^2*y + x*y^2 + y^3 + x^2 + x*y + y^2 + 1. 1; 0, 0; 1, 1, 1; 1, 1, 1, 1; 2, 2, 3, 2, 2; ... MAPLE read transforms; t1 := mul( mul( 1/(1-x^(i-j)*y^j), j=0..i), i=2..11): SERIES2(t1, x, y, 7); MATHEMATICA max = 12; gf = Product[1/(1 - x^(i - j)*y^j), {i, 2, max}, {j, 0, i}]; se = Series[gf, {x, 0, max}, {y, 0, max}] // Normal; t[n_, k_] := SeriesCoefficient[se, {x, 0, n}, {y, 0, k}]; Flatten[ Table[ t[n - k, k], {n, 0, max}, {k, 0, n}]] (* Jean-François Alcover, after Maple *) CROSSREFS Columns 0-6: A002865, A000041, A024786, A291553, A291589, A291590, A291596. Row sums: A060285. Cf. A005380, A054225. Sequence in context: A085962 A160821 A300225 * A072814 A196229 A191302 Adjacent sequences:  A060241 A060242 A060243 * A060245 A060246 A060247 KEYWORD nonn,nice,tabl,easy AUTHOR N. J. A. Sloane, Mar 22 2001 EXTENSIONS More terms from Vladeta Jovovic, Mar 23 2001 Edited by Christian G. Bower, Jan 08 2004 STATUS approved

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Last modified September 17 17:26 EDT 2021. Contains 347489 sequences. (Running on oeis4.)