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 A056858 Triangle of number of rises in restricted growth strings (RGS) for the set partitions of n. 3
 1, 1, 1, 1, 3, 1, 1, 6, 7, 1, 1, 10, 26, 14, 1, 1, 15, 71, 89, 26, 1, 1, 21, 161, 380, 267, 46, 1, 1, 28, 322, 1268, 1709, 732, 79, 1, 1, 36, 588, 3571, 8136, 6794, 1887, 133, 1, 1, 45, 1002, 8878, 31532, 44924, 24717, 4654, 221, 1, 1, 55, 1617, 20053, 104927, 234412, 221857, 84170, 11113, 364, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Number of rises s_{i+1} > s_i in the RGS [s_1, ..., s_n] for a set partition of {1, ..., n}, where s_i is the index of the subset containing i, s_1 = 1 and s_i <= 1 + max_{ji, x, 1), j=1..m+1)))     end: T:= n->(p-> seq(coeff(p, x, i), i=1..n))(b(n, 1, 0)): seq(T(n), n=1..12);  # Alois P. Heinz, Mar 24 2016 MATHEMATICA b[n_, i_, m_] := b[n, i, m] = Expand[If[n == 0, x, Sum[b[n - 1, j, Max[m, j]]*If[j > i, x, 1], {j, 1, m + 1}]]]; T[n_] := Function[p, Table[Coefficient[p, x, i], {i, 1, n}]][b[n, 1, 0]]; Table[T[n], {n, 1, 12}] // Flatten (* Jean-François Alcover, May 23 2016, after Alois P. Heinz *) CROSSREFS Cf. A000110 (row sums). Cf. A056857-A056863. Column 1 is triangular numbers (A000217); diagonal T(n, n-1) appears to be A001924. Sequence in context: A133713 A008278 A213735 * A137251 A158359 A046716 Adjacent sequences:  A056855 A056856 A056857 * A056859 A056860 A056861 KEYWORD easy,nonn,tabl AUTHOR Winston C. Yang (winston(AT)cs.wisc.edu), Aug 31 2000 EXTENSIONS More terms from Franklin T. Adams-Watters, Jun 08 2006 Clarified definition and edited comment and example, Joerg Arndt, Mar 05 2016 STATUS approved

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Last modified February 24 00:51 EST 2020. Contains 332195 sequences. (Running on oeis4.)