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 A127954 Triangle, A097805 * A127648. 1
 1, 0, 2, 0, 2, 3, 0, 2, 6, 4, 0, 2, 9, 12, 5, 0, 2, 12, 24, 20, 6, 0, 2, 15, 40, 50, 30, 7, 0, 2, 18, 60, 100, 90, 42, 8, 0, 2, 21, 84, 175, 210, 147, 56, 9, 0, 2, 24, 112, 280, 420, 392, 224, 72, 10 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Row sums = A045623 starting (1, 2, 5, 12, 28, 64, ...). Dropping the first column gives A128710. - Peter Bala, Mar 05 2013 T(n,k) is the number of ways to place n unlabeled balls into 2 boxes, make compositions of the integer number of balls in each box so that the total number of parts in both compositions is k. - Geoffrey Critzer, Sep 21 2013 LINKS FORMULA A097805 * A127648 as infinite lower triangular matrices. E.g.f.: 1/(1 - y*(x/(1-x)))^2. - Geoffrey Critzer, Sep 21 2013 EXAMPLE First few rows of the triangle are: 1; 0, 2; 0, 2, 3; 0, 2, 6, 4; 0, 2, 9, 12, 5; 0, 2, 12, 24, 20, 6; 0, 2, 15, 40, 50, 30, 7; ... T(4,3)=12. Place 4 unlabeled balls into 2 labeled boxes then make compositions of the integer number of balls in each box so that there are a total of 3 parts. /**** 3 ways since there are 3 compositions of 4 into 3 parts. */***  2 ways 1;1+2  and 1;2+1 **/**  2 ways 2;1+1  and 1+1;2. ***/*  2 ways as above. ****/  3 ways as above. 3+2+2+2+3=12. - Geoffrey Critzer, Sep 21 2013 MATHEMATICA nn=10; a=x/(1-x); CoefficientList[Series[1/(1-y a)^2, {x, 0, nn}], {x, y}]//Grid (* Geoffrey Critzer, Sep 21 2013 *) CROSSREFS Cf. A097805, A127648, A128710. Sequence in context: A198632 A060155 A209127 * A198061 A265583 A238156 Adjacent sequences:  A127951 A127952 A127953 * A127955 A127956 A127957 KEYWORD nonn,tabl AUTHOR Gary W. Adamson, Feb 09 2007 STATUS approved

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Last modified August 4 01:57 EDT 2020. Contains 336201 sequences. (Running on oeis4.)