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 A291532 Number of trees in all forests of (unlabeled) rooted identity trees with n vertices. 3
 0, 1, 1, 3, 4, 9, 19, 40, 84, 186, 413, 922, 2082, 4733, 10831, 24928, 57648, 133923, 312393, 731328, 1717784, 4047111, 9561517, 22647521, 53770164, 127941813, 305046676, 728688803, 1743752229, 4179697971, 10034077377, 24123567285, 58076419495, 139996849639 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 FORMULA a(n) = Sum_{k>=1} k * A227774(n+1,k). a(n) = Sum_{h=0..n} Sum_{t=0..n-h} t * A291529(n,h,t). EXAMPLE a(4) = 4: :   o   :   o  o   :     o     : :   |   :   |      :    / \    : :   o   :   o      :   o   o   : :   |   :   |      :   |       : :   o   :   o      :   o       : :   |   :          :           : :   o   :          :           : :       :          :           : MAPLE b:= proc(n, i, t) option remember; expand(`if`(n=0 or i=1,        `if`(n<2, x^(t*n), 0), b(n, i-1, t)+add(binomial(        b(i-1\$2, 0), j)*x^(t*j)*b(n-i*j, i-1, t), j=1..n/i)))     end: a:= n-> (p-> add(i*coeff(p, x, i), i=1..degree(p)))(b(n\$2, 1)): seq(a(n), n=0..35); CROSSREFS Cf. A004111, A005197, A227774, A291529. Sequence in context: A028344 A219680 A078010 * A110810 A247579 A282615 Adjacent sequences:  A291529 A291530 A291531 * A291533 A291534 A291535 KEYWORD nonn AUTHOR Alois P. Heinz, Aug 25 2017 STATUS approved

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Last modified August 13 02:09 EDT 2020. Contains 336441 sequences. (Running on oeis4.)