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 A115604 Triangle read by rows: T(n,k) is the number of partitions of n into odd parts in which the smallest part occurs k times (1<=k<=n). 0
 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 2, 1, 0, 1, 0, 0, 1, 2, 1, 1, 0, 1, 0, 0, 1, 2, 1, 2, 1, 0, 1, 0, 0, 1, 3, 2, 1, 1, 1, 0, 1, 0, 0, 1, 3, 3, 1, 1, 1, 1, 0, 1, 0, 0, 1, 4, 2, 2, 2, 1, 1, 1, 0, 1, 0, 0, 1, 5, 3, 2, 2, 1, 1, 1, 1, 0, 1, 0, 0, 1, 5, 4, 3, 2, 2, 1, 1, 1, 1, 0, 1, 0, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,22 COMMENTS Row sums yield A000009. T(n,1)=A087897(n+2). Sum(k*T(n,k),k=1..n)=A092268(n). LINKS FORMULA G.f.=G(t,x)=sum(tx^(2k-1)/[(1-tx^(2k-1))product(1-x^(2i-1), i=k+1..infinity)], k=1..infinity). EXAMPLE T(14,2)=4 because we have [9,3,1,1],[7,7],[7,5,1,1] and [3,3,3,3,1,1]. Triangle starts: 1; 0,1; 1,0,1; 1,0,0,1; 1,1,0,0,1; 1,1,1,0,0,1; 2,1,0,1,0,0,1; MAPLE g:=sum(t*x^(2*k-1)/(1-t*x^(2*k-1))/product(1-x^(2*i-1), i=k+1..40), k=1..40): gser:=simplify(series(g, x=0, 55)): for n from 1 to 15 do P[n]:=expand(coeff(gser, x^n)) od: for n from 1 to 15 do seq(coeff(P[n], t^j), j=1..n) od; # yields sequence in triangular form CROSSREFS Cf. A000009, A087897, A092268, A117408. Sequence in context: A293513 A015738 A308103 * A128617 A116488 A216601 Adjacent sequences:  A115601 A115602 A115603 * A115605 A115606 A115607 KEYWORD nonn,tabl AUTHOR Emeric Deutsch, Mar 13 2006 STATUS approved

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Last modified October 16 11:06 EDT 2019. Contains 328056 sequences. (Running on oeis4.)