A354659 - OEIS

%I #8 Mar 19 2023 07:39:05

%S 1,3,30,390,5928,98910,1757688,32683680,628884300,12428334215,

%T 250940544738,5156722096422,107538413657010,2270751678647100,

%U 48464836803383400,1044050265679857144,22675350105240015204,496034970650911331550,10920742396832034391590

%N A diagonal of triangle A354650: a(n) = A354650(n,n+1), for n >= 0.

%H Paul D. Hanna, <a href="/A354659/b354659.txt">Table of n, a(n) for n = 0..100</a>

%F a(n) = A354649(n,n+1), for n >= 0.

%F a(n) = A354650(n,n+1), for n >= 0.

%F a(n) ~ c * d^n / n^2, where d = 24.5759928778699928131449756... and c = 0.35661791857107638456206... - _Vaclav Kotesovec_, Mar 19 2023

%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+1),", "))

%Y Cf. A354649, A354650, A354658, A354660.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jun 02 2022