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 A000300 4th power of rooted tree enumerator: linear forests of 4 rooted trees. (Formerly M3479 N1414) 6
 1, 4, 14, 44, 133, 388, 1116, 3168, 8938, 25100, 70334, 196824, 550656, 1540832, 4314190, 12089368, 33911543, 95228760, 267727154, 753579420, 2123637318, 5991571428, 16923929406, 47857425416, 135478757308, 383929643780, 1089118243128, 3092612497260 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,2 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 = 4..500 FORMULA G.f.: B(x)^4 where B(x) is g.f. of 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-3)^4, x=0, n+1), x, n): seq(a(n), n=4..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, n/k}]; bb[n_] := bb[n] = Sum[b[k]*x^k, {k, 1, n}]; a[n_] := Coefficient[ Series[ bb[n - 3]^4, {x, 0, n + 1}], x, n]; Table[a[n], {n, 4, 31}] (* Jean-François Alcover, Jan 25 2013, translated from Alois P. Heinz's Maple program *) CROSSREFS Cf. A000081, A000106, A000242, A000343, A000395. Sequence in context: A118042 A006645 A094309 * A005323 A027831 A097894 Adjacent sequences:  A000297 A000298 A000299 * A000301 A000302 A000303 KEYWORD nonn AUTHOR EXTENSIONS More terms from Christian G. Bower, Nov 15 1999 STATUS approved

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Last modified November 19 08:51 EST 2017. Contains 294923 sequences.