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 A241500 Triangle T(n,k): number of ways of partitioning the n-element multiset {1,1,2,3,...,n-1} into exactly k nonempty parts, n>=1 and 1<=k<=n. 5
 1, 1, 1, 1, 2, 1, 1, 5, 4, 1, 1, 11, 16, 7, 1, 1, 23, 58, 41, 11, 1, 1, 47, 196, 215, 90, 16, 1, 1, 95, 634, 1041, 640, 176, 22, 1, 1, 191, 1996, 4767, 4151, 1631, 315, 29, 1, 1, 383, 6178, 21001, 25221, 13587, 3696, 526, 37, 1, 1, 767, 18916, 90055, 146140, 105042, 38409, 7638, 831, 46, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS FORMULA T(n,k) = S(n-1,k) + S(n-1,k-1) + C(k,2)*S(n-2,k), where S refers to Stirling numbers of the second kind (A008277), and C to binomial coefficients (A007318). EXAMPLE There are 58 ways to partition {1,1,2,3,4,5} into three nonempty parts. The first few rows are: 1; 1, 1; 1, 2, 1; 1, 5, 4, 1; 1, 11, 16, 7, 1; 1, 23, 58, 41, 11, 1; 1, 47, 196, 215, 90, 16, 1; 1, 95, 634, 1041, 640, 176, 22, 1; 1, 191, 1996, 4767, 4151, 1631, 315, 29, 1; 1, 383, 6178, 21001, 25221, 13587, 3696, 526, 37, 1; ... PROG (PARI) T(n, k) = stirling(n-1, k, 2) + stirling(n-1, k-1, 2) + binomial(k, 2)*stirling(n-2, k, 2); \\ Michel Marcus, Apr 24 2014 CROSSREFS The first five columns appear as A000012, A083329, A168583, A168584, A168585. Row sums give A035098. Sequence in context: A288620 A263324 A284949 * A152924 A220738 A284732 Adjacent sequences: A241497 A241498 A241499 * A241501 A241502 A241503 KEYWORD nonn,easy,tabl AUTHOR Andrew Woods, Apr 24 2014 STATUS approved

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Last modified March 31 20:59 EDT 2023. Contains 361673 sequences. (Running on oeis4.)