A283439 Hankel transform of A033434.

1, -3, -9, -6, 10, 25, 15, -21, -49, -28, 36, 81, 45, -55, -121, -66, 78, 169, 91, -105, -225, -120, 136, 289, 153, -171, -361, -190, 210, 441, 231, -253, -529, -276, 300, 625, 325, -351, -729, -378, 406, 841, 435, -465, -961, -496, 528, 1089, 561, -595, -1225

Offset: 0

Author

Paul Barry, Mar 07 2017

Keywords

• sign
• easy

Comments

a(n) modulo 2 is A131719(n+2).

Crossrefs

Cf. A131719, A033434.

Programs

Mathematica

CoefficientList[Series[(1 - 5*x + 2*x^3 - 3*x^4 + 2*x^5 - x^6)/((1 + x)*(1 - x + x^2)^3) ,{x, 0, 35}], x] (* Indranil Ghosh, Mar 08 2017 *)

PARI

print(Vec((1 - 5*x + 2*x^3 - 3*x^4 + 2*x^5 - x^6)/((1 + x)*(1 - x + x^2)^3) + O(x^36))); \\ Indranil Ghosh, Mar 08 2017

Formula

G.f.: (1 - 5*x + 2*x^3 - 3*x^4 + 2*x^5 - x^6)/((1 + x)*(1 - x + x^2)^3).

a(3*k) = (-1)^k*(k + 1)*(2*k + 1).

a(3*k + 1) = -(-1)^k*(k + 1)*(2*k + 3).

a(3*k + 2) = -(-1)^k*(k + 3)^2.

Extensions

More terms from Indranil Ghosh, Mar 08 2017