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A132311 Triangle read by rows: T(n,k) = number of partitions of binomial(n,k) into parts of the first n rows of Pascal's triangle, 0<=k<=n. 3
0, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 4, 7, 4, 1, 1, 6, 28, 28, 6, 1, 1, 11, 117, 318, 117, 11, 1, 1, 14, 388, 3344, 3344, 388, 14, 1, 1, 21, 1757, 71277, 290521, 71277, 1757, 21, 1, 1, 29, 8270, 2031198, 53679222, 53679222, 2031198, 8270, 29, 1, 1, 42, 40243 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

T(n,k) = T(n,n-k);

T(n,0) = 1 for n>0;

A000041(n) - 1 <= T(n,1) <= A000041(n) for n>1;

LINKS

Table of n, a(n) for n=0..57.

Index entries for triangles and arrays related to Pascal's triangle

EXAMPLE

A007318(4,2) = A007318(6,1) = 6:

T(4,2)=#{3+3,3+2+1,3+1+1+1,2+2+2,2+2+1+1,2+1+1+1+1,1+1+1+1+1+1}=7,

but T(6,1) = A000041(6) = 11.

CROSSREFS

Cf. A132312, A007318, A126257, A014631.

Sequence in context: A284992 A191687 A177254 * A254414 A199802 A121697

Adjacent sequences:  A132308 A132309 A132310 * A132312 A132313 A132314

KEYWORD

nonn,tabl

AUTHOR

Reinhard Zumkeller, Aug 18 2007

STATUS

approved

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Last modified May 22 15:05 EDT 2017. Contains 286874 sequences.