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%I #5 Aug 05 2016 18:19:43
%S 1,0,1,2,4,8,17,36,78,168,364,786,1700,3668,7916,17056,36729,78996,
%T 169772,364472,781814,1675464,3587660,7675722,16409240,35052552,
%U 74822496,159599700,340199178,724675528,1542673868,3281957116,6977971852,14827596904,31489490296,66837617960,141789447876,300636048724,637116434912,1349532001896,2857195771769,6046370298448
%N G.f. A(x) satisfies: 1 = ...(((((A(x) - x^2)^(1/2) - x^3)^(1/2) - x^4)^(1/2) - x^5)^(1/2) - x^6)^(1/2) -...- x^n)^(1/2) -..., an infinite series of nested square roots.
%C Compare definition with that of A274965.
%F G.f.: A(x) = G(x,x), where G(x,y) = x*y + G(x,x*y)^2 is the g.f. of A275670.
%F G.f.: A(x) = sqrt(F(x) - x), where F(x) is the g.f. of A274965.
%e G.f.: A(x) = 1 + x^2 + 2*x^3 + 4*x^4 + 8*x^5 + 17*x^6 + 36*x^7 + 78*x^8 + 168*x^9 + 364*x^10 + 786*x^11 + 1700*x^12 + 3668*x^13 + 7916*x^14 +...
%e The g.f. of related sequence A274965 begins:
%e A(x)^2 + x = 1 + x + 2*x^2 + 4*x^3 + 9*x^4 + 20*x^5 + 46*x^6 + 104*x^7 + 238*x^8 + 540*x^9 + 1228*x^10 + 2780*x^11 + 6289*x^12 +...
%o (PARI) {a(n) = my(A=1 +x*O(x^n)); for(k=0, n, A = A^2 + x^(n+2-k)); polcoeff(A, n)}
%o for(n=0, 60, print1(a(n), ", "))
%Y Cf. A274965.
%Y Antidiagonal sums of triangle A275670.
%K nonn
%O 0,4
%A _Paul D. Hanna_, Aug 05 2016
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