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 A116663 Triangle read by rows: T(n,k) = number of partitions of n into odd parts and having exactly k parts equal to 1 (n>=0, 1<=k<=n). 0
 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 2, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 2, 2, 1, 1, 1, 1, 0, 1, 0, 0, 1, 3, 2, 2, 2, 1, 1, 1, 1, 0, 1, 0, 0, 1, 3, 3, 2, 2, 2, 1, 1, 1, 1, 0, 1, 0, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,46 COMMENTS Row sums yield A000009. T(n,0)=A087897(n). Column k has g.f.=x^k/Product(1-x^(2j-1), j=2..infinity) (all columns are basically identical). Sum(k*T(n,k),k=0..n)=A036469(n). LINKS FORMULA G.f.=1/[(1-tx)*Product(1-x^(2j-1), j=2..infinity)]. EXAMPLE T(10,1)=2 because the only partitions of 10 into odd parts and having exactly 1 part equal to 1 are [9,1] and [3,3,3,1]. Triangle starts: 1; 0,1; 0,0,1; 1,0,0,1; 0,1,0,0,1; MAPLE g:=1/(1-t*x)/product(1-x^(2*j-1), j=2..30): gser:=simplify(series(g, x=0, 18)): P[0]:=1: for n from 1 to 14 do P[n]:=sort(coeff(gser, x^n)) od: for n from 0 to 14 do seq(coeff(P[n], t, j), j=0..n) od; # yields sequence in triangular form CROSSREFS Cf. A000009, A087897, A036469. Sequence in context: A238450 A251926 A037908 * A258940 A319659 A050372 Adjacent sequences:  A116660 A116661 A116662 * A116664 A116665 A116666 KEYWORD nonn,tabl AUTHOR Emeric Deutsch, Feb 22 2006 STATUS approved

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Last modified October 18 02:23 EDT 2019. Contains 328135 sequences. (Running on oeis4.)