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 A036721 G.f. satisfies A(x) = 1 + x*cycle_index(Sym(5), A(x)). 11
 1, 1, 1, 2, 4, 9, 20, 47, 112, 277, 693, 1766, 4547, 11852, 31146, 82534, 220149, 590834, 1593951, 4320723, 11761394, 32138301, 88121176, 242383729, 668607115, 1849194691, 5126800907, 14245679652, 39666239726, 110661514973, 309280533011, 865839831118 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Also the number of rooted trees where each node has at most 5 children. [Patrick Devlin, Apr 30 2012] LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 FORMULA a(n) = Sum_{j=1..5} A244372(n,j) for n>0, a(0) = 1. - Alois P. Heinz, Sep 19 2017 MAPLE b:= proc(n, i, t, k) option remember; `if`(n=0, 1,       `if`(i<1, 0, add(binomial(b((i-1)\$2, k\$2)+j-1, j)*        b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))     end: a:= n-> `if`(n=0, 1, b(n-1\$2, 5\$2)): seq(a(n), n=0..35);  # Alois P. Heinz, Sep 20 2017 CROSSREFS Cf. A000081, A036717, A036718, A036719, A036720, A036722, A182378, A244372, A292553, A292554, A292555, A292556. Column k=5 of A299038. Sequence in context: A095980 A036619 A036620 * A014267 A089405 A091500 Adjacent sequences:  A036718 A036719 A036720 * A036722 A036723 A036724 KEYWORD nonn AUTHOR STATUS approved

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Last modified May 26 04:01 EDT 2018. Contains 304588 sequences. (Running on oeis4.)