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Column 3 of A052250.
2

%I #17 Nov 09 2020 04:43:41

%S 1,3,6,13,27,63,148,363,912,2330,6036,15825,41865,111636,299736,

%T 809513,2197728,5994219,16416748,45129396,124479270,344403494,

%U 955557780,2658061560,7411457963,20710700277,57992124810,162691293718,457219737027,1287065977413

%N Column 3 of A052250.

%C Also expansion of cube of g.f. for A051573. - _Alois P. Heinz_, Oct 23 2009

%H Alois P. Heinz, <a href="/A052251/b052251.txt">Table of n, a(n) for n = 3..700</a>

%F a(n) ~ c * d^n / n^(3/2), where d = A051491 = 2.9557652856519949747148175241..., c = 0.195489104191039910520879642... . - _Vaclav Kotesovec_, Sep 05 2014

%p with(numtheory): A81:= proc(n) option remember; `if`(n<2, n, (add(add(d*A81(d), d=divisors(j)) *A81(n-j), j=1..n-1))/ (n-1)) end: b:= proc(n) option remember; -`if`(n<0, 1, add(b(n-i) *A81(i+1), i=1..n+1)) end: B:= proc(n) add(b(i) *x^i, i=0..n) end: a:= n-> coeff(B(n)^3, x, n-3): seq(a(n), n=3..35); # _Alois P. Heinz_, Oct 23 2009

%t A81[n_] := A81[n] = If[n < 2, n, Sum[Sum[d A81[d], {d, Divisors[j]}] A81[n - j], {j, 1, n - 1}]/(n - 1)];

%t b[n_] := b[n] = -If[n < 0, 1, Sum[b[n - i] A81[i + 1], {i, 1, n + 1}]];

%t B[n_] := Sum[b[i] x^i, {i, 0, n}];

%t T[n_, k_] := Coefficient[B[n]^k, x, n - k];

%t a[n_] := T[n, 3];

%t a /@ Range[3, 35] (* _Jean-François Alcover_, Nov 09 2020, after _Alois P. Heinz_ *)

%Y Cf. A051573, A000081. - _Alois P. Heinz_, Oct 23 2009

%Y Cf. A051491.

%K nonn

%O 3,2

%A _David Broadhurst_, Feb 05 2000

%E More terms from _Alois P. Heinz_, Oct 23 2009