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A036721 G.f. satisfies A(x) = 1 + x*cycle_index(Sym(5), A(x)). 10
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

Joerg Arndt, The a(6) = 20 rooted trees with 5 nodes and out-degrees <= 5

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.

Sequence in context: A095980 A036619 A036620 * A014267 A089405 A091500

Adjacent sequences:  A036718 A036719 A036720 * A036722 A036723 A036724

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified October 18 03:13 EDT 2017. Contains 293486 sequences.