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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

Table of n, a(n) for n=1..90.

Henry Bottomley, Partition calculators using java applets

Index entries for sequences related to partitions

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,changed

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified January 16 19:49 EST 2019. Contains 319206 sequences. (Running on oeis4.)