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 A257490 Irregular triangle read by rows in which the n-th row lists multinomials (A036040) for partitions of 2n which have only even parts in Abramowitz-Stegun ordering. 5
 1, 1, 3, 1, 15, 15, 1, 28, 35, 210, 105, 1, 45, 210, 630, 1575, 3150, 945, 1, 66, 495, 462, 1485, 13860, 5775, 13860, 51975, 51975, 10395, 1, 91, 1001, 3003, 3003, 45045, 42042, 105105, 45045, 630630, 525525, 315315, 1576575, 945945, 135135 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The length of row n is given by A000041(n). Each entry in this irregular triangle is the quotient of the respective entries in A257468 and A096162, which is the multinomial called M_3 in Abramowitz-Stegun. Has the same structure as the triangles in A036036, A096162, A115621 and A257468. LINKS M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy], pp. 831-832. EXAMPLE Brackets group all partitions of the same length when there is more than one partition. n/m  1    2          3           4    5 1:   1 2:   1    3 3:   1   15         15 4:   1  [28  35]   210         105 5:   1  [45 210]  [630 1575]  3150  945 ... n = 6:  1 [66 495 462] [1485 13860 5775] [13860 51975] 51975  0395 Replacing the bracketed numbers by their sums yields the triangle of A156289. MATHEMATICA (* triangle2574868[] and triangle096162[] are defined as functions triangle[] in the respective sequences A257468 and A096162 *) triangle[n_] := triangle257468[n]/triangle096162[n] a[n_] := Flatten[triangle[n]] a[7] (* data *) CROSSREFS Cf. A000041, A036040, A036036, A096162, A115621, A156289, A257468. Sequence in context: A193966 A113378 A178657 * A156289 A095922 A263632 Adjacent sequences:  A257487 A257488 A257489 * A257491 A257492 A257493 KEYWORD nonn,tabf AUTHOR Hartmut F. W. Hoft, Apr 26 2015 EXTENSIONS Edited by Wolfdieter Lang, May 11 2015 STATUS approved

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Last modified December 3 15:15 EST 2021. Contains 349463 sequences. (Running on oeis4.)