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 A059025 Triangle of Stirling numbers of order 6. 4
 1, 1, 1, 1, 1, 1, 1, 462, 1, 1716, 1, 4719, 1, 11440, 1, 25883, 1, 56134, 1, 118456, 2858856, 1, 245480, 23279256, 1, 502588, 124710300, 1, 1020680, 551496660, 1, 2061709, 2181183147, 1, 4149752, 8021782197, 1, 8333153, 28051272535 (list; graph; refs; listen; history; text; internal format)
 OFFSET 6,8 COMMENTS The number of partitions of the set N, |N|=n, into k blocks, all of cardinality greater than or equal to 6. This is the 6-associated Stirling number of the second kind. This is entered as a triangular array. The entries S_6(n,k) are zero for 6k>n, so these values are omitted. Initial entry in sequence is S_6(6,1). Rows are of lengths 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, ... REFERENCES L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 222. J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 76. LINKS Table of n, a(n) for n=6..44. A. E. Fekete, Apropos two notes on notation, Amer. Math. Monthly, 101 (1994), 771-778. FORMULA S_r(n+1, k)=k S_r(n, k)+binomial(n, r-1)S_r(n-r+1, k-1) for this sequence, r=6. G.f.: Sum_{n>=0, k>=0} S_r(n,k)*u^k*t^n/n! = exp(u(e^t - Sum_{i=0..r-1} t^i/i!)). EXAMPLE There are 462 ways of partitioning a set N of cardinality 12 into 2 blocks each of cardinality at least 6, so S_6(12,2)=462. MATHEMATICA S6[n_ /; 6 <= n <= 11, 1] = 1; S6[n_, k_] /; 1 <= k <= Floor[n/6] := S6[n, k] = k*S6[n-1, k] + Binomial[n-1, 5]*S6[n-6, k-1]; S6[_, _] = 0; Flatten[ Table[ S6[n, k], {n, 6, 24}, {k, 1, Floor[n/6]}]] (* Jean-François Alcover, Feb 21 2012 *) CROSSREFS Cf. A008299, A059022, A059023, A059024. Sequence in context: A138956 A107121 A101734 * A267200 A348899 A094380 Adjacent sequences: A059022 A059023 A059024 * A059026 A059027 A059028 KEYWORD nonn,tabf,nice AUTHOR Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Dec 14 2000 STATUS approved

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Last modified July 20 16:01 EDT 2024. Contains 374459 sequences. (Running on oeis4.)