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 A000526 Partially labeled trees with n nodes (5 of which are labeled). (Formerly M5387 N2340) 9
 125, 1296, 8716, 47787, 232154, 1040014, 4395772, 17781210, 69498964, 264248924, 982218072, 3582421612, 12857819052, 45515994861, 159205157535, 551049504784, 1889714853263, 6427147635062, 21698583468717 (list; graph; refs; listen; history; text; internal format)
 OFFSET 5,1 REFERENCES J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 138. 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). LINKS Vincenzo Librandi, Table of n, a(n) for n = 5..200 FORMULA G.f.: A(x) = B(x)^5*(125-204*B(x)+118*B(x)^2-24*B(x)^3)/(1-B(x))^7, where B(x) is g.f. for rooted trees with n nodes, cf. A000081. 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-4)^5* (125-204*B(n-4) +118*B(n-4)^2 -24*B(n-4)^3)/ (1-B(n-4))^7, x=0, n+1), x, n): seq(a(n), n=5..23); # Alois P. Heinz, Aug 21 2008 MATHEMATICA b[n_] := b[n] = If[n <= 1, n, Sum[k*b[k]*s[n-1, k], {k, 1, n-1}]/(n-1)]; s[n_, k_] := s[n, k] = Sum[b[n + 1 - j*k], {j, 1, Quotient[n, k]}]; B[n_] := B[n] = Sum[b[k]*x^k, {k, 1, n}]; a[n_] := SeriesCoefficient[B[n-4]^5*(125 - 204*B[n-4] + 118*B[n-4]^2 - 24*B[n-4]^3)/(1 - B[n-4])^7, {x, 0, n}]; Table[a[n], {n, 5, 23}] (* Jean-François Alcover, Mar 20 2014, after Alois P. Heinz *) CROSSREFS Cf. A000055, A000107, A000243, A000269, A000444, A000485, A000524, A000525. Sequence in context: A204795 A243240 A237713 * A016971 A030082 A017043 Adjacent sequences:  A000523 A000524 A000525 * A000527 A000528 A000529 KEYWORD nonn AUTHOR EXTENSIONS More terms from Vladeta Jovovic, Oct 19 2001 STATUS approved

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Last modified January 20 14:40 EST 2019. Contains 319333 sequences. (Running on oeis4.)