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A090367 Shifts 1 place left under the INVERT transform of the BINOMIAL transform of the self-convolution cube of this sequence.

%I A090367 #12 Jun 04 2018 03:12:09
%S A090367 1,1,5,34,276,2509,24739,259815,2873376,33207790,398897289,4960652325,
%T A090367 63676368387,841741913795,11438028248093,159536511439266,
%U A090367 2281321298635427,33411684617642665,500761214428795093,7674842860939188928,120209960716130232745
%N A090367 Shifts 1 place left under the INVERT transform of the BINOMIAL transform of the self-convolution cube of this sequence.
%H A090367 Alois P. Heinz, <a href="/A090367/b090367.txt">Table of n, a(n) for n = 0..200</a>
%F A090367 G.f.: A(x) = 1/(1 - A(x/(1-x))^3*x/(1-x) ).
%p A090367 bintr:= proc(p) local b; b:= proc(n) option remember;
%p A090367            add(p(k) *binomial(n,k), k=0..n) end
%p A090367         end:
%p A090367 invtr:= proc(p) local b; b:= proc(n) option remember;
%p A090367            `if`(n<1, 1, add(b(n-i) *p(i-1), i=1..n+1)) end
%p A090367         end:
%p A090367 s:= proc(n) option remember; add(a(i)*a(n-i), i=0..n) end:
%p A090367 b:= invtr(bintr(n-> add(s(i)*a(n-i), i=0..n))):
%p A090367 a:= n-> `if`(n<0, 0, b(n-1)):
%p A090367 seq(a(n), n=0..25);  # _Alois P. Heinz_, Jun 28 2012
%t A090367 m = 25; A[_] = 1; Do[A[x_] = 1/(1 - A[x/(1-x)]^3*(x/(1-x))) + O[x]^m // Normal, {m}]; CoefficientList[A[x], x] (* _Jean-François Alcover_, Jun 04 2018 *)
%o A090367 (PARI) {a(n)=local(A); if(n<0,0,A=1+x+x*O(x^n); for(k=1,n,B=subst(A^3,x,x/(1-x))/(1-x)+x*O(x^n); A=1+x*A*B);polcoeff(A,n,x))}
%Y A090367 Cf. A090365, A090366.
%K A090367 nonn
%O A090367 0,3
%A A090367 _Paul D. Hanna_, Nov 26 2003