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A036718
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Number of rooted trees where each node has at most 4 children.
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1
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1, 1, 1, 2, 4, 9, 19, 45, 106, 260, 643, 1624, 4138, 10683, 27790, 72917, 192548, 511624, 1366424, 3666930, 9881527, 26730495, 72556208, 197562840, 539479354, 1477016717, 4053631757, 11149957667, 30732671572, 84871652538, 234802661446
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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LINKS
| F. Ruskey, Information on Rooted Trees
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FORMULA
| G.f. satisfies A(x) = 1 + x*cycle_index(Sym(4), A(x)).
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MAPLE
| A := 1; f := proc(n) global A; local A2, A3, A4; A2 := subs(x=x^2, A); A3 := subs(x=x^3, A); A4 := subs(x=x^4, A);
coeff(series( 1+x*( (A^4+3*A2^2+8*A*A3+6*A^2*A2+6*A4)/2 ), x, n+1), x, n); end;
for n from 1 to 50 do A := series(A+f(n)*x^n, x, n +1); od: A;
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CROSSREFS
| Cf. A036717.
Sequence in context: A036612 A036613 A036614 * A134964 A052328 A133228
Adjacent sequences: A036715 A036716 A036717 * A036719 A036720 A036721
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Better description from Frank Ruskey (ruskey(AT)cs.uvic.ca), Sep 23 2000
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