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 A000395 6th power of rooted tree enumerator; number of linear forests of 6 rooted trees. (Formerly M4175 N1739) 6
 1, 6, 27, 104, 369, 1236, 3989, 12522, 38535, 116808, 350064, 1039896, 3068145, 9004182, 26314773, 76652582, 222705603, 645731148, 1869303857, 5404655358, 15611296146, 45060069406, 129989169909, 374843799786, 1080624405287 (list; graph; refs; listen; history; text; internal format)
 OFFSET 6,2 REFERENCES J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 150. 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 Alois P. Heinz, Table of n, a(n) for n = 6..1000 FORMULA G.f.: B(x)^6 where B(x) is g.f. of A000081. a(n) ~ 6 * A187770 * A051491^n / n^(3/2). - Vaclav Kotesovec, Jan 03 2021 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-5)^6, x=0, n+1), x, n): seq(a(n), n=6..30); # 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-5]^6, {x, 0, n}]; Table[a[n], {n, 6, 30}] (* Jean-François Alcover, Oct 13 2014, after Alois P. Heinz *) CROSSREFS Column 6 of A339067. Cf. A000081, A000106, A000242, A000300, A000343. Sequence in context: A124641 A169793 A054457 * A005325 A099623 A119852 Adjacent sequences: A000392 A000393 A000394 * A000396 A000397 A000398 KEYWORD nonn AUTHOR EXTENSIONS More terms from Christian G. Bower, Nov 15 1999 STATUS approved

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Last modified March 28 05:31 EDT 2023. Contains 361577 sequences. (Running on oeis4.)