A275691 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.

1, 0, 1, 2, 4, 8, 17, 36, 78, 168, 364, 786, 1700, 3668, 7916, 17056, 36729, 78996, 169772, 364472, 781814, 1675464, 3587660, 7675722, 16409240, 35052552, 74822496, 159599700, 340199178, 724675528, 1542673868, 3281957116, 6977971852, 14827596904, 31489490296, 66837617960, 141789447876, 300636048724, 637116434912, 1349532001896, 2857195771769, 6046370298448

Offset: 0

Author

Paul D. Hanna, Aug 05 2016

Keywords

• nonn

Comments

Compare definition with that of A274965.

Examples

			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 +...
The g.f. of related sequence A274965 begins:
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 +...
		

Crossrefs

Cf. A274965.

Antidiagonal sums of triangle A275670.

Programs

PARI

{a(n) = my(A=1 +x*O(x^n)); for(k=0, n, A = A^2 + x^(n+2-k)); polcoeff(A, n)}
for(n=0, 60, print1(a(n), ", "))

Formula

G.f.: A(x) = G(x,x), where G(x,y) = x*y + G(x,x*y)^2 is the g.f. of A275670.

G.f.: A(x) = sqrt(F(x) - x), where F(x) is the g.f. of A274965.