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 A200144 The number of multinomial coefficients, based on a set of partitions of n into m positions, divisible by m entirely. 0
 1, 1, 2, 3, 6, 7, 14, 17, 27, 34, 55, 64, 100, 121, 167, 213, 296, 354, 489, 594, 776, 964, 1254, 1511, 1951, 2378, 2986, 3643, 4564, 5483, 6841, 8245, 10099, 12190, 14862, 17783, 21636, 25849, 31184 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS If n is prime, then the number of multinomial coefficients, based on a set of partitions of n at position m, divided by m entirely, less 1 than the number of partitions of numbers for all m. LINKS EXAMPLE n=7;   Set of partitions of n into m=4 parts [1,1,1,4] [1,1,2,3] [1,2,2,2] number of different parts [3,1] [2,1,1] [1,3] Multinomial coefficient,  divisible by m 4!/(4*(1!*3!))=1 4!/(4*(2!*1!*1!))=2 4!/(4*(1!*3!))=1 Set of partitions of n into m=7 parts [1,1,1,1,1,1,1] number of different parts [7] Multinomial coefficient,  divisible by m 7!/(7*(7!))=1/7 PROG (Maxima) /* count number of partitions of n into m parts */ b(n, m):=if n

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Last modified October 18 02:23 EDT 2019. Contains 328135 sequences. (Running on oeis4.)