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A036658
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Number of n-node rooted unlabeled trees with exactly 3 edges at root and otherwise out-degree <=2.
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3
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0, 0, 0, 0, 1, 1, 3, 6, 14, 29, 68, 147, 337, 757, 1734, 3953, 9113, 20988, 48645, 112909, 263084, 614201, 1438001, 3373253, 7930660, 18679005, 44075988, 104173194, 246604137, 584620470, 1387879434, 3299067379, 7851736348
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,7
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LINKS
| Index entries for sequences related to rooted trees
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FORMULA
| Let G036656(x) = g.f. for A036656. G.f.: x^3*cycle_index(S3, G036656), where cycle_index(Sk, f) means apply the cycle index for the symmetric group S_k to f(x).
E.g. cycle_index(S2, f) = (1/2!)*(f^2+subs(x=x^2, f), cycle_index(S3, f) = (1/3!)*(f^3+3*subs(x=x^2, f)*f+2*subs(x=x^3, f)).
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MAPLE
| CI2 := proc(f) (1/2)*(f^2+subs(x=x^2, f)); end; CI3 := proc(f) (1/6)*(f^3+3*subs(x=x^2, f)*f+2*subs(x=x^3, f)); end;
N := 40: G036658 := series(x^3*CI3(G036656), x, N); A036658 := n->coeff(G036658, x, n);
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CROSSREFS
| Sequence in context: A038359 A038360 A084174 * A077067 A083797 A192672
Adjacent sequences: A036655 A036656 A036657 * A036659 A036660 A036661
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Corrected May 03 2000 - N. J. A. Sloane (njas(AT)research.att.com).
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