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Expansion of g.f. exp(Sum_{n>=1} A061163(n)*t^n/n).
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%I #10 Oct 10 2024 15:38:41

%S 1,630,891285,1654468410,3510378217530,8062345916976876,

%T 19512437110988445005,49011998362940952903570,

%U 126572647331085036145017230,333972707681972700439601909620,896449866774126643993004643968130,2440147600216903599224231295951096900,6719826062906171491705313637277701498260

%N Expansion of g.f. exp(Sum_{n>=1} A061163(n)*t^n/n).

%F O.g.f.(t) = g satisfies the algebraic equation of order 30 in the form: 1 + Sum_{n=1..30} p(n,t)*g^n = 0, where p(n,t) are polynomials of t of order n with integer coefficients. For example p(15,t) = 2*t^9*(77558760*t^6 - 1112153600*t^5 - 2309989894*t^4 + 784164428*t^3 + 6287761*t^2 - 9848*t + 3)

%p Digits:=40;

%p series(exp(630*t*hypergeom([1, 1, 11/10, 13/10, 17/10, 19/10], [5/4, 3/2, 7/4, 2, 2], 3125*t)),t=0,16);

%p 1,seq(coeff(%,t^kk),kk=1..15);

%Y Cf. A061163.

%K nonn

%O 0,2

%A _Karol A. Penson_, Oct 07 2024