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 A000343 5th power of rooted tree enumerator; number of linear forests of 5 rooted trees. (Formerly M3901 N1601) 6
 1, 5, 20, 70, 230, 721, 2200, 6575, 19385, 56575, 163952, 472645, 1357550, 3888820, 11119325, 31753269, 90603650, 258401245, 736796675, 2100818555, 5990757124, 17087376630, 48753542665, 139155765455, 397356692275, 1135163887190, 3244482184720, 9277856948255 (list; graph; refs; listen; history; text; internal format)
 OFFSET 5,2 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 = 5..750 FORMULA G.f.: B(x)^5 where B(x) is g.f. of A000081. a(n) ~ 5 * 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-4)^5, x=0, n+1), x, n): seq(a(n), n=5..29); # 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_] := Coefficient[Series[B[n-4]^5, {x, 0, n+1}], x, n]; Table[a[n], {n, 5, 32}] (* Jean-François Alcover, Mar 05 2014, after Alois P. Heinz *) CROSSREFS Column 5 of A339067. Cf. A000081, A000106, A000242, A000300, A000395. Sequence in context: A089094 A080930 A169792 * A005324 A304011 A243869 Adjacent sequences: A000340 A000341 A000342 * A000344 A000345 A000346 KEYWORD nonn AUTHOR EXTENSIONS More terms from Christian G. Bower, Nov 15 1999 STATUS approved

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Last modified March 28 03:48 EDT 2023. Contains 361577 sequences. (Running on oeis4.)