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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

%I

%S 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,

%T 14,388,3344,3344,388,14,1,1,21,1757,71277,290521,71277,1757,21,1,1,

%U 29,8270,2031198,53679222,53679222,2031198,8270,29,1,1,42,40243

%N 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.

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

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

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

%H <a href="/index/Pas#Pascal">Index entries for triangles and arrays related to Pascal's triangle</a>

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

%e 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,

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

%Y Cf. A132312, A007318, A126257, A014631.

%K nonn,tabl

%O 0,8

%A _Reinhard Zumkeller_, Aug 18 2007

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Last modified November 17 16:08 EST 2019. Contains 329241 sequences. (Running on oeis4.)