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A322241 G.f.: exp( Sum_{n>=1} A084605(n)^2 * x^n/n ), where A084605(n) is the central coefficient in (1 + x + 4*x^2)^n.

%I A322241 #4 Dec 08 2018 09:16:25
%S A322241 1,1,41,249,6305,77569,1665321,27724889,574252417,10958980929,
%T A322241 228679916905,4671350051321,99292476904609,2107949882690241,
%U A322241 45658568907254505,993562984208479193,21876513296218002433,484448162130512673665,10812975015547281792937,242647271141110287979513,5477046865641884201456033
%N A322241 G.f.: exp( Sum_{n>=1} A084605(n)^2 * x^n/n ), where A084605(n) is the central coefficient in (1 + x + 4*x^2)^n.
%C A322241 Compare to: exp( Sum_{n>=1} A084605(n) * x^n/n ) = (1-x - sqrt(1 - 2*x - 15*x^2))/(8*x^2), the g.f. of A091147.
%C A322241 Sequence A322240(n) = A084605(n)^2 has generating function 1 / AGM(1 + 15*x, sqrt((1 - 9*x)*(1 - 25*x)) ).
%e A322241 G.f.: A(x) = 1 + x + 41*x^2 + 249*x^3 + 6305*x^4 + 77569*x^5 + 1665321*x^6 + 27724889*x^7 + 574252417*x^8 + 10958980929*x^9 + 228679916905*x^10 + ...
%e A322241 such that
%e A322241 log(A(x)) = x + 81*x^2/2 + 625*x^3/3 + 21025*x^4/4 + 314721*x^5/5 + 8071281*x^6/6 + 155975121*x^7/7 + 3685097025*x^8/8 + ... + A084605(n)^2 * x^n/n + ...
%e A322241 RELATED SERIES.
%e A322241 The g.f. of A084605 equals the series
%e A322241 1/sqrt(1 - 2*x - 15*x^2) = 1 + x + 9*x^2 + 25*x^3 + 145*x^4 + 561*x^5 + 2841*x^6 + 12489*x^7 + 60705*x^8 + 281185*x^9 + ... + A084605(n) * x^n/n + ...
%o A322241 (PARI) {a(n)=if(n==0, 1, polcoeff(exp(sum(m=1, n, polcoeff(1/sqrt(1 - 2*x - 15*x^2 +x*O(x^m)), m)^2 *x^m/m)+x*O(x^n)), n))}
%o A322241 for(n=0,30,print1(a(n),", "))
%Y A322241 Cf. A322240, A084605.
%K A322241 nonn
%O A322241 0,3
%A A322241 _Paul D. Hanna_, Dec 08 2018