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 A026836 Triangular array T read by rows: T(n,k) = number of partitions of n into distinct parts, the greatest being k, for k=1,2,...,n. 6
 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 2, 1, 1, 1, 0, 0, 0, 1, 2, 1, 1, 1, 0, 0, 0, 1, 2, 2, 1, 1, 1, 0, 0, 0, 1, 2, 2, 2, 1, 1, 1, 0, 0, 0, 0, 2, 3, 2, 2, 1, 1, 1, 0, 0, 0, 0, 2, 3, 3, 2, 2, 1, 1, 1, 0, 0, 0, 0, 1, 3, 4, 3, 2, 2, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,25 COMMENTS Conjecture: A199918(n) = Sum_{k=1..n} (-1)^(n-k) T(n,k). - George Beck, Jan 13 2019 LINKS Henry Bottomley, Partition calculators using java applets FORMULA T(n, k) = A070936(n-k, k-1) = A053632(k-1, n-k) = T(n-1, k-1)+T(n-2k+1, k-1). - Henry Bottomley, May 12 2002 T(n, k) = coefficient of x^n in x^k*Product_{i=1..k-1} (1+x^i). - Vladeta Jovovic, Aug 07 2003 EXAMPLE Triangle begins: [1] [0, 1] [0, 1, 1] [0, 0, 1, 1] [0, 0, 1, 1, 1] [0, 0, 1, 1, 1, 1] [0, 0, 0, 2, 1, 1, 1] [0, 0, 0, 1, 2, 1, 1, 1] [0, 0, 0, 1, 2, 2, 1, 1, 1] [0, 0, 0, 1, 2, 2, 2, 1, 1, 1] [0, 0, 0, 0, 2, 3, 2, 2, 1, 1, 1] [0, 0, 0, 0, 2, 3, 3, 2, 2, 1, 1, 1] [0, 0, 0, 0, 1, 3, 4, 3, 2, 2, 1, 1, 1] [0, 0, 0, 0, 1, 3, 4, 4, 3, 2, 2, 1, 1, 1] ... - N. J. A. Sloane, Nov 09 2018 MAPLE with(combinat); f2:=proc(n) local i, j, p, t0, t1, t2; t0:=Array(1..n, 0); t1:=partition(n); p:=numbpart(n); for i from 1 to p do t2:=t1[i]; if nops(convert(t2, set))=nops(t2) then # now have a partition t2 of n into distinct parts t0[t2[-1]]:=t0[t2[-1]]+1; od: [seq(t0[j], j=1..n)]; end proc; for n from 1 to 12 do lprint(f2(n)); od: # N. J. A. Sloane, Nov 09 2018 CROSSREFS If seen as a square array then transpose of A070936 and visible form of A053632. Central diagonal and those to the right of center are A000009 as are row sums. Sequence in context: A059607 A176724 A015318 * A089052 A284606 A284019 Adjacent sequences:  A026833 A026834 A026835 * A026837 A026838 A026839 KEYWORD nonn,tabl AUTHOR STATUS approved

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Last modified September 30 11:55 EDT 2020. Contains 337439 sequences. (Running on oeis4.)