cp's OEIS Frontend

A052252 Column 4 of A052250.

%I A052252 #19 Nov 09 2020 04:45:01
%S A052252 1,4,10,24,55,132,322,804,2051,5304,13886,36716,97882,262756,709658,
%T A052252 1926748,5255707,14396048,39580338,109190052,302148814,838449236,
%U A052252 2332652648,6505071080,18180441512,50914047384,142853059922,401517522844,1130400537667,3187335556064
%N A052252 Column 4 of A052250.
%C A052252 Also expansion of 4th power of g.f. for A051573. - _Alois P. Heinz_, Oct 23 2009
%H A052252 Alois P. Heinz, <a href="/A052252/b052252.txt">Table of n, a(n) for n = 4..500</a>
%F A052252 a(n) ~ c * d^n / n^(3/2), where d = A051491 = 2.9557652856519949747148..., c = 0.17246782327675280347707... . - _Vaclav Kotesovec_, Sep 06 2014
%p A052252 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)^4, x, n-4): seq(a(n), n=4..35); # _Alois P. Heinz_, Oct 23 2009
%t A052252 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 A052252 b[n_] := b[n] = -If[n < 0, 1, Sum[b[n - i] A81[i + 1], {i, 1, n + 1}]];
%t A052252 B[n_] := Sum[b[i] x^i, {i, 0, n}];
%t A052252 T[n_, k_] := Coefficient[B[n]^k, x, n - k];
%t A052252 a[n_] := T[n, 4];
%t A052252 a /@ Range[4, 35] (* _Jean-François Alcover_, Nov 09 2020, after _Alois P. Heinz_ *)
%Y A052252 Cf. A051573, A000081. - _Alois P. Heinz_, Oct 23 2009
%K A052252 nonn
%O A052252 4,2
%A A052252 _David Broadhurst_, Feb 05 2000
%E A052252 More terms from _Alois P. Heinz_, Oct 23 2009