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 A290355 The sixth Euler transform of the sequence with g.f. 1+x. 3
 1, 1, 6, 21, 91, 336, 1337, 5026, 19193, 71769, 268272, 992676, 3659116, 13400426, 48863017, 177299790, 640713627, 2305930966, 8268556438, 29544196129, 105215495691, 373523546056, 1322096328899, 4666327388034, 16425341129078, 57667752483279, 201967215942032 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Also the number of 6-level rooted trees with n leaves. All n leaves are in level 6. a(2) = 6: :    o      o      o      o      o      o :    |      |      |      |      |     ( ) :    o      o      o      o      o     o o :    |      |      |      |     ( )    | | :    o      o      o      o     o o    o o :    |      |      |     ( )    | |    | | :    o      o      o     o o    o o    o o :    |      |     ( )    | |    | |    | | :    o      o     o o    o o    o o    o o :    |     ( )    | |    | |    | |    | | :    o     o o    o o    o o    o o    o o :   ( )    | |    | |    | |    | |    | | :   o o    o o    o o    o o    o o    o o LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 B. A. Huberman and T. Hogg, Complexity and adaptation, Evolution, games and learning (Los Alamos, N.M., 1985). Phys. D 22 (1986), no. 1-3, 376-384. FORMULA G.f.: Product_{j>0} 1/(1-x^j)^A007714(j). MAPLE with(numtheory): b:= proc(n, k) option remember; `if`(n<2, 1, `if`(k=0, 0, add(       add(b(d, k-1)*d, d=divisors(j))*b(n-j, k), j=1..n)/n))     end: a:= n-> b(n, 6): seq(a(n), n=0..30); MATHEMATICA b[n_, k_]:=b[n, k]=If[n<2, 1, If[k==0, 0, Sum[Sum[b[d, k - 1]*d, {d, Divisors[j]}] b[n - j, k], {j, n}]/n]]; Table[b[n, 6], {n, 0, 30}] (* Indranil Ghosh, Jul 30 2017, after Maple code *) CROSSREFS Column k=6 of A290353. Cf. A007714. Sequence in context: A304187 A005498 A002222 * A006359 A001553 A009247 Adjacent sequences:  A290352 A290353 A290354 * A290356 A290357 A290358 KEYWORD nonn AUTHOR Alois P. Heinz, Jul 28 2017 STATUS approved

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Last modified December 6 19:31 EST 2019. Contains 329809 sequences. (Running on oeis4.)