A227315 G.f.: sqrt(1 + 2*Sum_{n>=1} 2^n*x^(n^2)).

1, 2, -2, 4, -6, 20, -60, 184, -586, 1908, -6284, 21032, -71260, 243928, -842456, 2931984, -10272586, 36203996, -128262540, 456526584, -1631731284, 5854243512, -21075615496, 76110581584, -275644817124, 1000906315656, -3643229263480, 13290759624336, -48586176336056, 177955767765936, -652966762175152

Offset

0,2

Links

Table of n, a(n) for n=0..30.

Example

G.f.: A(x) = 1 + 2*x - 2*x^2 + 4*x^3 - 6*x^4 + 20*x^5 - 60*x^6 + 184*x^7 - 586*x^8 + 1908*x^9 - 6284*x^10 + 21032*x^11 - 71260*x^12 +...
where
A(x)^2 = 1 + 4*x + 8*x^4 + 16*x^9 + 32*x^16 + 64*x^25 + 128*x^36 + 256*x^49 +...

Mathematica

With[{nn=30}, CoefficientList[Series[Sqrt[1+2Sum[2^n x^n^2, {n, nn}]], {x, 0, nn}], x]] (* Harvey P. Dale, May 04 2015 *)

Prog

(PARI) {a(n)=polcoeff(sqrt(1+sum(k=1, n, 2*2^k*x^(k^2))+x*O(x^n)), n)}
for(n=0, 36, print1(a(n), ", "))

Crossrefs

Cf. A227312.

Sequence in context: A358366 A069925 A357951 * A080611 A171421 A072707

Adjacent sequences: A227312 A227313 A227314 * A227316 A227317 A227318

Keyword

sign

Author

Paul D. Hanna, Jul 06 2013

Status

approved