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 A132311 Triangle read by rows: T(n,k) is the number of partitions of binomial(n,k) into parts of the first n rows of Pascal's triangle, 0<=k<=n. 4
 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, 74464383, 19465193506, 147286801214, 19465193506, 74464383, 40243, 42, 1 (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 Alois P. Heinz, Rows n = 0..18, flattened 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. Triangle T(n,k) begins:   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;   ... CROSSREFS Cf. A132312, A007318, A126257, A014631. Sequence in context: A191687 A322190 A177254 * A254414 A199802 A297347 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 October 20 19:28 EDT 2020. Contains 337909 sequences. (Running on oeis4.)