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Central terms of triangle A361050.
5

%I #8 Mar 19 2023 04:56:06

%S 1,5,244,19090,1839075,199363606,23320604384,2876887986028,

%T 369107300988219,48807370374419910,6610055144592717246,

%U 912769451975745598299,128087096344387852459658,18219369599509083643661044,2621701165622760015979876800,381039123615762485580377457688

%N Central terms of triangle A361050.

%H Paul D. Hanna, <a href="/A361538/b361538.txt">Table of n, a(n) for n = 1..51</a>

%F a(n) = A361050(2*n-1,n-1) for n >= 1.

%F a(n) ~ c * d^n / n^2, where d = 166.5794571279985... and c = 0.000249393859904361... - _Vaclav Kotesovec_, Mar 19 2023

%o (PARI) {A361050(n,k) = my(A=[0, 1]); for(i=1, n, A = concat(A, 0);

%o A[#A] = polcoeff(y/x - prod(m=1, #A, (1 - x^m) * (1 - x^m*Ser(A)) * (1 - x^(m-1)/Ser(A)) * (1 - x^(2*m-1)*Ser(A)^2) * (1 - x^(2*m-1)/Ser(A)^2) ), #A-4) );

%o polcoeff(polcoeff(H=Ser(A),n,x),k,y)}

%o for(n=1, 16, print1(A361050(2*n-1,n-1), ", "))

%Y Cf. A361050.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Mar 18 2023