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Self-convolution square root of the even bisection of A274965.
3

%I #10 Aug 16 2016 13:30:06

%S 1,1,4,19,92,446,2150,10280,48761,229558,1073278,4986624,23037102,

%T 105877968,484337300,2206188412,10010589904,45264063504,204016241794,

%U 916898737038,4109984712933,18379240912034,82012499946246,365245641944278,1623757696702586,7207073607368924,31941896126213722,141377838141158888,624983649220555836,2759711619634526196,12173102200970091434

%N Self-convolution square root of the even bisection of A274965.

%C The g.f. of A274965 equals G(x,1), where G(x,y) = x*y + G(x,x*y)^2 is the g.f. of A275670.

%C First negative term is at a(646).

%H Paul D. Hanna, <a href="/A275751/b275751.txt">Table of n, a(n) for n = 0..1024</a>

%e G.f.: A(x) = 1 + x + 4*x^2 + 19*x^3 + 92*x^4 + 446*x^5 + 2150*x^6 + 10280*x^7 + 48761*x^8 + 229558*x^9 + 1073278*x^10 + 4986624*x^11 + 23037102*x^12 +...

%e where

%e A(x)^2 = 1 + 2*x + 9*x^2 + 46*x^3 + 238*x^4 + 1228*x^5 + 6289*x^6 + 31924*x^7 + 160694*x^8 + 802642*x^9 + 3980916*x^10 +...+ A274965(2*n)*x^n +...

%o (PARI) {a(n) = my(A,B=1); for(k=0, 2*n, B = B^2 + x^(2*n+1-k) +O(x^(2*n+1))); A = sqrt( (B + subst(B,x,-x))/2 ); polcoeff(A, 2*n)}

%o for(n=0, 30, print1(a(n), ", "))

%Y Cf. A274965, A275752.

%K sign

%O 0,3

%A _Paul D. Hanna_, Aug 14 2016