OFFSET
0,4
COMMENTS
Row sums of A174135.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
FORMULA
a(n) ~ c * d^n / n^(3/2), where d = A051491 = 2.9557652856519949747148..., c = 0.8603881121111431... . - Vaclav Kotesovec, Sep 10 2014
In the asymptotics above the constant c = A187770 * (A051491 - 1). - Vladimir Reshetnikov, Aug 12 2016
MAPLE
with(numtheory):
t:= proc(n) option remember; local d, j; `if`(n<=1, n,
(add(add(d*t(d), d=divisors(j))*t(n-j), j=1..n-1))/(n-1))
end:
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<2, 0,
add(b(n-i*j, i-1)*binomial(t(i)+j-1, j), j=0..n/i)))
end:
a:= n-> b(n, n):
seq(a(n), n=0..32); # Alois P. Heinz, May 17 2013
MATHEMATICA
t[n_] := t[n] = If[n <= 1, n, Sum[Sum[d*t[d], {d, Divisors[j]}]*t[n-j], {j, 1, n-1}]/(n-1)]; b[n_, i_] := b[n, i] = If[n == 0, 1, If[i<2, 0, Sum[b[n-i*j, i-1]*Binomial[t[i]+j-1, j], {j, 0, n/i}]]]; a[n_] := b[n, n]; Table[a[n] // FullSimplify, {n, 0, 32}] (* Jean-François Alcover, Mar 19 2014, after Alois P. Heinz *)
t[1] = 1; t[n_] := t[n] = Sum[k t[k] t[n - k m]/(n-1), {k, n-1}, {m, (n-1)/k}]; a[n_] := t[n+1] - t[n]; Table[a[n], {n, 0, 32}] (* Vladimir Reshetnikov, Aug 12 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 26 2010
STATUS
approved