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%I #8 Jun 08 2022 02:31:08
%S 1,3,27,340,5070,83559,1472261,27205308,520974180,10257025240,
%T 206469879462,4232227325352,88073315164471,1856404180514940,
%U 39560345751767970,851083806077023888,18462636758298743712,403459312929849694791,8874351725505564788350
%N A diagonal of triangle A354650: a(n) = A354650(n,n), for n >= 0.
%H Paul D. Hanna, <a href="/A354658/b354658.txt">Table of n, a(n) for n = 0..100</a>
%F a(n) = -A354649(n,n), for n >= 0.
%F a(n) = A354650(n,n), for n >= 0.
%F a(n) ~ c * d^n / n^2, where d = 24.575992877869992813144975... and c = 0.285171824264368179079895... - _Vaclav Kotesovec_, Jun 08 2022
%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=0,20,print1(A354650(n,n),", "))
%Y Cf. A354649, A354650, A354659, A354660.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jun 02 2022