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A316386
Binomial transform of [0, 1, 2, -3, -4, 5, 6, -7, -8, ...].
1
0, 1, 4, 6, 0, -20, -48, -56, 0, 144, 320, 352, 0, -832, -1792, -1920, 0, 4352, 9216, 9728, 0, -21504, -45056, -47104, 0, 102400, 212992, 221184, 0, -475136, -983040, -1015808, 0, 2162688, 4456448, 4587520, 0, -9699328, -19922944, -20447232, 0, 42991616
OFFSET
0,3
FORMULA
a(n) = n * A009545(n).
a(n+1) = a(n) + A140230(n).
From Colin Barker, Jul 01 2018: (Start)
G.f.: x*(1 - 2*x^2) / (1 - 2*x + 2*x^2)^2.
a(n) = 4*a(n-1) - 8*a(n-2) + 8*a(n-3) - 4*a(n-4) for n>3.
a(n) = i*(((1-i)^n - (1+i)^n)*n) / 2 where i=sqrt(-1).
(End)
MAPLE
seq(coeff(series(x*(1-2*x^2)/(1-2*x+2*x^2)^2, x, n+1), x, n), n=0..45); # Muniru A Asiru, Jul 01 2018
MATHEMATICA
CoefficientList[Series[x (1 - 2 x^2)/(1 - 2 x + 2 x^2)^2, {x, 0, 41}], x] (* Michael De Vlieger, Jul 01 2018 *)
LinearRecurrence[{4, -8, 8, -4}, {0, 1, 4, 6}, 42] (* Robert G. Wilson v, Jul 15 2018 *)
PROG
(PARI) concat(0, Vec(x*(1 - 2*x^2) / (1 - 2*x + 2*x^2)^2 + O(x^40))) \\ Colin Barker, Jul 01 2018
CROSSREFS
Sequence in context: A224273 A285444 A285584 * A288422 A268437 A265685
KEYWORD
sign,easy
AUTHOR
Paul Curtz, Jul 01 2018
EXTENSIONS
More terms from Colin Barker, Jul 01 2018
STATUS
approved