A301436 G.f. A(x) satisfies: 1 = Sum_{n>=0} ( 2*(1+x)^n - A(x) )^n / 2^(n+1).

1, 6, 50, 1582, 82722, 5842550, 511261682, 52903385886, 6290859281538, 843328959011622, 125706002934030898, 20617322695573745742, 3689811206934015405474, 715633021826704924420758, 149544785675949258192968178, 33502338836970792659941911358, 8011296279710787237594088464898, 2036927238948023349890031708437830, 548778491694092921577420334962662962, 156179940994829385561873698156273034606

Offset

0,2

Links

Paul D. Hanna, Table of n, a(n) for n = 0..50

Formula

G.f.: 1 = Sum_{n>=0} 2^n * (1+x)^(n^2) / (2 + (1+x)^n * A(x))^(n+1).

Example

G.f.: A(x) = 1 + 6*x + 50*x^2 + 1582*x^3 + 82722*x^4 + 5842550*x^5 + 511261682*x^6 + 52903385886*x^7 + 6290859281538*x^8 + ...
such that
1 = 1/2  +  (2*(1+x) - A(x))/2^2  +  (2*(1+x)^2 - A(x))^2/2^3  +  (2*(1+x)^3 - A(x))^3/2^4  +  (2*(1+x)^4 - A(x))^4/2^5  +  (2*(1+x)^5 - A(x))^5/2^6 + ...
Also,
1 = 1/(2 + A(x))  +  2*(1+x)/(2 + (1+x)*A(x))^2  +  2^2*(1+x)^4/(2 + (1+x)^2*A(x))^3  +  2^3*(1+x)^9/(2 + (1+x)^3*A(x))^4  +  2^4*(1+x)^16/(2 + (1+x)^4*A(x))^5  +  2^5*(1+x)^25/(2 + (1+x)^5*A(x))^6  + ...

Crossrefs

Cf. A303653, A301465.

Sequence in context: A008380 A196905 A066303 * A136383 A043084 A335704

Adjacent sequences: A301433 A301434 A301435 * A301437 A301438 A301439

Keyword

nonn

Author

Paul D. Hanna, Mar 24 2018

Status

approved