A275752 - OEIS

%I #7 Aug 16 2016 13:25:18

%S 1,2,8,36,166,770,3574,16560,76516,352498,1619014,7414134,33855996,

%T 154181234,700333366,3173299648,14345094004,64704125888,291235313046,

%U 1308229210186,5865335253474,26248821086374,117265700856282,523010482541564,2328947839518852,10354971182171076,45973304229373220,203824525466826232,902455230607927616,3990584636812405052,17624255201680536016

%N Self-convolution square root of the odd 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.

%H Paul D. Hanna, <a href="/A275752/b275752.txt">Table of n, a(n) for n = 0..1024</a>

%e G.f.: A(x) = 1 + 2*x + 8*x^2 + 36*x^3 + 166*x^4 + 770*x^5 + 3574*x^6 + 16560*x^7 + 76516*x^8 + 352498*x^9 + 1619014*x^10 + 7414134*x^11 + 33855996*x^12 +...

%e where

%e A(x)^2 = 1 + 4*x + 20*x^2 + 104*x^3 + 540*x^4 + 2780*x^5 + 14180*x^6 + 71688*x^7 + 359452*x^8 + 1788988*x^9 + 8844064*x^10 +...+ A274965(2*n+1)*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+2))); A = sqrt( (B - subst(B,x,-x))/(2*x) ); polcoeff(A, 2*n)}

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

%Y Cf. A274965, A275751.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Aug 14 2016