A247256 Exponential generating function = (1+x)^(1-x^2).

1, 1, 0, -6, -12, 20, 300, 252, -3024, -36720, 106560, 110880, 12212640, -125629920, 1005286464, -16865735040, 252900345600, -3575747185920, 58447092395520, -1014901444454400, 18218754479923200, -346655486035998720, 6952232946445839360, -145913061049673702400, 3205301440394904238080

Offset

0,4

Links

Table of n, a(n) for n=0..24.

Formula

a(n) ~ 2 * (-1)^n * n! / n^2 * (1 + 4*log(n)/n). - Vaclav Kotesovec, Nov 30 2014

Example

(1+x)^(1-x^2) = 1 + x - x^3 - 1/2*x^4 + 1/6*x^5 + 5/12*x^6 + 1/20*x^7 - 3/40*x^8 - 17/168*x^9 + 37/1260*x^10 + 1/360*x^11 + 257/10080*x^12 - ...

Mathematica

CoefficientList[Series[(1+x)^(1-x^2), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Nov 30 2014 *)

Prog

(PARI) Vec(serlaplace((1+x+O(x^25))^(1-x^2)))

Crossrefs

Cf. A005727, A007120, A247212.

Sequence in context: A141808 A144187 A303481 * A292951 A240989 A366564

Adjacent sequences: A247253 A247254 A247255 * A247257 A247258 A247259

Keyword

sign

Author

Franklin T. Adams-Watters, Nov 29 2014

Status

approved