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 A111724 Number of partitions of an n-set with an even number of blocks of size 1. 9
 0, 2, 1, 11, 21, 117, 428, 2172, 10727, 59393, 345335, 2143825, 14038324, 96834090, 700715993, 5305041715, 41910528809, 344714251149, 2945819805408, 26107419715988, 239556359980239, 2272364911439153, 22252173805170347, 224666265799310801, 2335958333831561032 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..576 FORMULA E.g.f.: cosh(x)*exp(exp(x)-1-x). More generally, e.g.f. for number of partitions of an n-set with an even number of blocks of size k is cosh(x^k/k!)*exp(exp(x)-1-x^k/k!). MAPLE b:= proc(n, t) option remember; `if`(n=0, t, add(b(n-j,       `if`(j=1, 1-t, t))*binomial(n-1, j-1), j=1..n))     end: a:= n-> b(n, 1): seq(a(n), n=1..30);  # Alois P. Heinz, May 10 2016 MATHEMATICA Rest[ Range[0, 24]! CoefficientList[ Series[ Cosh[x]Exp[Exp[x] - 1 - x], {x, 0, 23}], x]] (* Robert G. Wilson v *) PROG (Python) from sympy.core.cache import cacheit from sympy import binomial @cacheit def b(n, t): return t if n==0 else sum(b(n - j, (1 - t if j==1 else t))*binomial(n - 1, j - 1) for j in range(1, n + 1)) def a(n): return b(n, 1) print([a(n) for n in range(1, 51)]) # Indranil Ghosh, Aug 10 2017 CROSSREFS Cf. A097514, A113235, A063083, A062282, A111723, A111752, A111753. Sequence in context: A300455 A270264 A305877 * A184299 A080371 A151337 Adjacent sequences:  A111721 A111722 A111723 * A111725 A111726 A111727 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, Nov 17 2005 EXTENSIONS More terms from Robert G. Wilson v, Nov 22 2005 STATUS approved

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Last modified November 30 19:02 EST 2021. Contains 349424 sequences. (Running on oeis4.)