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A000525
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Partially labeled rooted trees with n nodes (4 of which are labeled).
(Formerly M5329 N2317)
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7
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64, 625, 4016, 21256, 100407, 439646, 1823298, 7258228, 27983518, 105146732, 386812476, 1398023732, 4977320988, 17492710572, 60790051789, 209179971147, 713533304668, 2415061934763, 8117293752058, 27111950991825, 90039381031273
(list; graph; refs; listen; history; internal format)
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OFFSET
| 4,1
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REFERENCES
| J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 134.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Index entries for sequences related to rooted trees
Index entries for sequences related to trees
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FORMULA
| G.f.: A(x) = B(x)^4*(64-79*B(x)+36*B(x)^2-6*B(x)^3)/(1-B(x))^7, where B(x) is g.f. for rooted trees with n nodes, cf. A000081.
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MAPLE
| b:= proc(n) option remember; if n<=1 then n else add(k*b(k)* s(n-1, k), k=1..n-1)/(n-1) fi end: s:= proc(n, k) option remember; add(b(n+1-j*k), j=1..iquo(n, k)) end: B:= proc(n) option remember; add (b(k)*x^k, k=1..n) end: a:= n-> coeff (series (B(n-3)^4* (64-79*B(n-3)+ 36*B(n-3)^2- 6*B(n-3)^3)/ (1-B(n-3))^7, x=0, n+1), x, n): seq (a(n), n=4..24); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 21 2008]
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CROSSREFS
| Cf. A000081, A000107, A000243, A000269, A000444, A000485, A000524, A000526.
Cf. A042977.
Sequence in context: A177757 A200788 A045789 * A067476 A179810 A138332
Adjacent sequences: A000522 A000523 A000524 * A000526 A000527 A000528
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 19 2001
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