A223027 G.f.: sqrt( 1 + Sum_{n>=1} 4*x^(n^2) ).

1, 2, -2, 4, -8, 24, -72, 224, -720, 2370, -7940, 27020, -93128, 324424, -1140512, 4041024, -14416030, 51737020, -186663414, 676656868, -2463300660, 9001715448, -33009329056, 121427520528, -447970371792, 1657029908094, -6144260440620, 22834249359960, -85037438715936

Offset

0,2

Links

Table of n, a(n) for n=0..28.

Example

 G.f.: A(x) = 1 + 2*x - 2*x^2 + 4*x^3 - 8*x^4 + 24*x^5 - 72*x^6 + 224*x^7 - 720*x^8 + 2370*x^9 - 7940*x^10 +...
such that
A(x)^2 = 1 + 4*x + 4*x^4 + 4*x^9 + 4*x^16 + 4*x^25 + 4*x^36 + 4*x^49 +...+ 4*x^(n^2) +...

Prog

 (PARI) {a(n)=polcoeff(sqrt(1+4*sum(k=1, sqrtint(n)+1, x^(k^2))+x*O(x^n)), n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Sequence in context: A259813 A121853 A064451 * A325514 A032440 A145869

Adjacent sequences: A223024 A223025 A223026 * A223028 A223029 A223030

Keyword

sign

Author

Paul D. Hanna, Mar 15 2013

Status

approved