%I #10 Sep 30 2023 18:02:34
%S 1,30,340,2530,14595,70737,301070,1157820,4100785,13563010,42321840,
%T 125586440,356621070,973989030,2569116330,6567458520,16317741975,
%U 39504992395,93390535840,215983566780,489454806785,1088433416785,2378160809610,5111208572940,10816601842950
%N Column 3 of triangle A354650: a(n) = A354650(n,3), for n >= 1.
%H Paul D. Hanna, <a href="/A354656/b354656.txt">Table of n, a(n) for n = 1..100</a>
%F a(n) = (-1)^n * A354649(n,3), for n >= 1.
%F a(n) = A354650(n,3), for n >= 1.
%o (PARI) {A354650(n,k) = my(A=[1+y]); for(i=1,n, A = concat(A,0);
%o A[#A] = polcoeff(y + sum(m=0,sqrtint(2*#A+9), (-1)^m * x^(m*(m-1)/2) * (1 - x^(2*m+1)) * Ser(A)^(m*(m+1)/2) ),#A-1) );
%o polcoeff(A[n+1],k,y)}
%o for(n=1,30,print1(A354650(n,3),", "))
%Y Cf. A354649, A354650, A354655, A354657.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Jun 02 2022