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 A335788 Expansion of e.g.f. 2*sec(exp(x)-1) - 2*tan(exp(x)-1) - exp(x). 1
 1, 1, 3, 11, 49, 263, 1675, 12417, 105183, 1002475, 10616589, 123679907, 1571831251, 21640964933, 320872742611, 5097445680435, 86377624918593, 1555173730665199, 29646960589439139, 596571563234557361, 12636340495630310359 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n) is the number of ways to partition {1,2,...,n} into any number of blocks, then order the blocks so that the set of least elements of the blocks is an alternating permutation. LINKS Michael De Vlieger, Table of n, a(n) for n = 0..199 FORMULA a(n) = Sum_{k=1..n} Stirling2(n,k)*A001250(k). E.g.f.: B(exp(x)-1) where B(x) = 2(tan(x) + sec(x))-1-x. a(n) ~ 8 * n! / ((Pi+2) * log(1 + Pi/2)^(n+1)). - Vaclav Kotesovec, Jun 24 2020 MATHEMATICA nn = 20; a[x_] := Tan[x] + Sec[x]; b[x_] := 2 a[x] - 1 - x; Range[0, nn]! CoefficientList[Series[b[Exp[x] - 1], {x, 0, nn}], x] (* Second program: *) Array[Abs[-1 + Sum[4 StirlingS2[#, k] Abs[PolyLog[-k, I]], {k, #}]] &, 21, 0] (* Michael De Vlieger, Aug 02 2021, after Jean-François Alcover at A001250 *) CROSSREFS Cf. A001250, A317022. Sequence in context: A356291 A001339 A307030 * A012316 A261600 A331617 Adjacent sequences: A335785 A335786 A335787 * A335789 A335790 A335791 KEYWORD nonn AUTHOR Geoffrey Critzer, Jun 23 2020 STATUS approved

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Last modified May 19 07:43 EDT 2024. Contains 372666 sequences. (Running on oeis4.)