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 A249619 Triangle T(m,n) = number of permutations of a multiset with m elements and signature corresponding to n-th integer partition (A194602). 2
 1, 1, 2, 1, 6, 3, 1, 24, 12, 4, 6, 1, 120, 60, 20, 30, 5, 10, 1, 720, 360, 120, 180, 30, 60, 6, 90, 15, 20, 1, 5040, 2520, 840, 1260, 210, 420, 42, 630, 105, 140, 7, 210, 21, 35, 1, 40320, 20160, 6720, 10080, 1680, 3360, 336, 5040, 840, 1120, 56 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS This triangle shows the same numbers in each row as A036038 and A078760 (the multinomial coefficients), but in this arrangement the multisets in column n correspond to the n-th integer partition in the infinite order defined by A194602. Triangle begins:   n     0    1    2    3   4   5  6   7   8   9 10 m 0       1 1       1 2       2    1 3       6    3    1 4      24   12    4    6   1 5     120   60   20   30   5  10  1 6     720  360  120  180  30  60  6  90  15  20  1 Row lengths: A000041 (partition numbers), Row sums: A005651 Columns: 0: A000142 (factorials), 1: A001710, 2: A001715, 3: A133799, 4: A001720, 6: A001725, 10: A001730, 14: A049388 Last in row: end-2: A037955 after 1 term mismatch, end-1: A001405, end: A000012 The rightmost columns form the triangle A173333:   n       0      1     2     4    6  10  14  21      (A000041(1,2,3...)-1) m 1         1 2         2      1 3         6      3     1 4        24     12     4     1 5       120     60    20     5    1 6       720    360   120    30    6   1 7      5040   2520   840   210   42   7   1 8     40320  20160  6720  1680  336  56   8   1 A249620 shows the number of partitions of the same multisets. A187783 shows the number of permutations of special multisets. LINKS Tilman Piesk, Triangle rows m=0..25, flattened Tilman Piesk, Illustration of the multisets for m=0..6 CROSSREFS Cf. A036038, A078760, A005651, A005651, A249620, A000041, A173333. Sequence in context: A138533 A173333 A221915 * A222159 A221623 A096334 Adjacent sequences:  A249616 A249617 A249618 * A249620 A249621 A249622 KEYWORD nonn,tabf AUTHOR Tilman Piesk, Nov 04 2014 STATUS approved

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Last modified October 13 18:57 EDT 2019. Contains 327981 sequences. (Running on oeis4.)