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%I #13 Jul 27 2022 02:45:27
%S 1,25,397,5125,58813,626725,6356749,62315125,596370205,5610245125,
%T 52128987181,480061573525,4392455087677,40002549209125,
%U 363080219023693,3287474035532725,29714233445499229,268240649382317125
%N Expansion of g.f. exp( Sum_{n>=1} (2^n+3^n)^2*x^n/n ).
%C More generally, for integer m>=0 and real p and q,
%C exp( Sum_{n>=1} (p^n+q^n)^m*x^n/n ) = 1/Product_{k=0..m} (1 - p^k*q^(m-k)*x)^C(m,k).
%H Stefano Spezia, <a href="/A174515/b174515.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (25,-228,900,-1296).
%F O.g.f.: 1/((1-4*x)*(1-6*x)^2*(1-9*x)).
%F From _Stefano Spezia_, Jul 21 2022: (Start)
%F a(n) = 25*a(n-1) - 228*a(n-2) + 900*a(n-3) - 1296*a(n-4) for n > 3.
%F a(n) = (9^(2+n) - 4^(2+n) - 5*6^(1+n)*(2 + n))/5. (End)
%o (PARI) {a(n)=polcoeff(exp(sum(m=1,n+1,((2^m+3^m)^2*x^m/m)+x*O(x^n))),n)}
%Y Cf. A007689.
%K nonn,easy
%O 0,2
%A _Paul D. Hanna_, Apr 22 2010