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 A227119 Number of ways to select a set partition, P of {1,2,...,n} and then select a subset, S of {1,2,...,n} such that for all i in {1,2,...,n-1} if i and i+1 are in S then i and i+1 are in different blocks of P. 1
 1, 2, 7, 31, 163, 985, 6676, 49918, 406820, 3580011, 33764544, 339222866, 3612046889, 40588278875, 479542299692, 5938050050297, 76848380886090, 1036869475470365, 14553056889254517, 212063804824260167, 3202482669648363619, 50039504959872274840 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..200 FORMULA E.g.f.: exp(A''(x) - 1) where A(x) is the e.g.f. for A000045. EXAMPLE a(2) = 7: We can choose the set partition {{1,2}} and then choose the subsets: {}, {1}, {2}; we can choose the set partition {{1},{2}} and then the subsets: {}, {1}, {2}, {1,2}. MAPLE F:= combinat[fibonacci]: a:= proc(n) option remember; `if`(n=0, 1, add(       binomial(n-1, j-1)*F(j+2)*a(n-j), j=1..n))     end: seq(a(n), n=0..30);  # Alois P. Heinz, Aug 06 2017 MATHEMATICA nn=15; Range[0, nn]!CoefficientList[Series[Exp[-1+Exp[x/2]Cosh[5^(1/2)x/2] +3Exp[x/2]Sinh[5^(1/2)x/2]/5^(1/2)], {x, 0, nn}], x] (* Geoffrey Critzer, Jul 01 2013 *) PROG (Python) from sympy.core.cache import cacheit from sympy import fibonacci as F, binomial @cacheit def a(n): return 1 if n==0 else sum([binomial(n - 1, j - 1)*F(j + 2)*a(n - j) for j in xrange(1, n + 1)]) print map(a, xrange(31)) # Indranil Ghosh, Aug 07 2017, after Maple code CROSSREFS Sequence in context: A125275 A007446 A277396 * A002872 A105216 A260532 Adjacent sequences:  A227116 A227117 A227118 * A227120 A227121 A227122 KEYWORD nonn AUTHOR Geoffrey Critzer, Jul 01 2013 STATUS approved

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Last modified June 19 11:14 EDT 2019. Contains 324219 sequences. (Running on oeis4.)