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A026821 Triangular array T read by rows: T(n,k) = number of partitions of n into distinct parts, the least being k, for k=1,2,...,n. 0
1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 2, 1, 0, 0, 0, 1, 2, 1, 1, 0, 0, 0, 1, 3, 1, 1, 0, 0, 0, 0, 1, 3, 2, 1, 1, 0, 0, 0, 0, 1, 5, 2, 1, 1, 0, 0, 0, 0, 0, 1, 5, 3, 1, 1, 1, 0, 0, 0, 0, 0, 1, 7, 3, 2, 1, 1, 0, 0, 0, 0, 0, 0, 1, 8, 4, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,16

COMMENTS

T(n,1) = A025147(n-1). Sum(k*T(n,k),k=1..n) = A092265(n). - Emeric Deutsch, Feb 24 2006

LINKS

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

FORMULA

T(n, k) = T(n-k, k+1) + ... + T(n-k, n-k) for 1<=k<=m and T(n, k)=0 for m+1<=k<=n-1, where m=[ (n-1)/2 ]; T(n, n)=1 for n >= 1.

G.f.: sum(t^j*x^j*product(1+x^i,i=j+1..infinity),j=1..infinity). - Emeric Deutsch, Feb 24 2006

EXAMPLE

T(11,2)=3 because we have [9,2],[6,3,2] and [5,4,2].

Triangle starts:

1;

0,1;

1,0,1;

1,0,0,1;

1,1,0,0,1;

MAPLE

g:=sum(t^j*x^j*product(1+x^i, i=j+1..50), j=1..50): gser:=simplify(series(g, x=0, 18)): for n from 1 to 14 do P[n]:=sort(coeff(gser, x^n)) od: seq(seq(coeff(P[n], t^j), j=1..n), n=1..14); # Emeric Deutsch, Feb 24 2006

CROSSREFS

Cf. A025147, A092265.

Sequence in context: A284585 A280456 A103633 * A039964 A035172 A110174

Adjacent sequences:  A026818 A026819 A026820 * A026822 A026823 A026824

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified July 24 18:02 EDT 2017. Contains 289776 sequences.