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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

Index entries for sequences related to rooted trees

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-Fran├žois 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

N. J. A. Sloane

EXTENSIONS

More terms from Christian G. Bower, Nov 15 1999

STATUS

approved

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Last modified August 16 11:20 EDT 2017. Contains 290623 sequences.