cp's OEIS Frontend

A359715 Column 2 of triangle A359670; a(n) = A359670(n+2,2) for n >= 0.

%I A359715 #5 Jan 18 2023 14:54:22
%S A359715 1,12,68,284,998,3092,8724,22904,56679,133516,301664,657368,1387854,
%T A359715 2849168,5704476,11166464,21415632,40312176,74593476,135864792,
%U A359715 243872632,431835140,755039948,1304589104,2229192801,3769452152,6311385252,10469412968,17214152072
%N A359715 Column 2 of triangle A359670; a(n) = A359670(n+2,2) for n >= 0.
%C A359715 The g.f. G(x,y) of triangle A359670 satisfies: G(x,y) = 1/[Sum_{n=-oo..+oo} (-1)^n * (x*y*G(x,y) + x^n)^n].
%o A359715 (PARI) {a(n) = my(A=1); for(i=1,n+2,
%o A359715 A = 1/sum(m=-#A,#A, (-1)^m * (x*y*A + x^m + x*O(x^(n+2)) )^m ) );
%o A359715 polcoeff( polcoeff( A,n+2,x),2,y)}
%o A359715 for(n=0,30, print1( a(n),", "))
%o A359715 (PARI) {a(n) = my(A=[1]); for(i=1,n+2, A = concat(A,0);
%o A359715 A[#A] = polcoeff(-y + sum(m=-#A,#A, (-1)^m * x^m * (y*Ser(A) + x^(m-1))^(m+1) )/(-y),#A-1,x) ); polcoeff( A[n+3],2,y)}
%o A359715 for(n=0,30, print1(a(n),", "))
%Y A359715 Cf. A359670.
%K A359715 nonn
%O A359715 0,2
%A A359715 _Paul D. Hanna_, Jan 17 2023