A025966 Expansion of 1/((1-2x)(1-4x)(1-6x)(1-8x)).

1, 20, 260, 2800, 27216, 248640, 2182720, 18656000, 156544256, 1296655360, 10641146880, 86744985600, 703688298496, 5688011079680, 45855653642240, 368956766617600, 2964331947687936, 23790756829593600

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (20,-140,400,-384).

Crossrefs

Fourth column of triangle A075497.

Cf. A016283, A075510.

Programs

Mathematica

CoefficientList[Series[1/((1-2x)(1-4x)(1-6x)(1-8x)),{x,0,40}],x] (* Harvey P. Dale, Apr 13 2019 *)

PARI

Vec(1/((1-2*x)*(1-4*x)*(1-6*x)*(1-8*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Formula

a(n) = (2^n)*stirling2(n+4, 4), n>=0, with stirling2(n, m)=A008277(n, m).

a(n) = (-2^n+24*4^n-81*6^n+64*8^n)/3!.

G.f.: 1/((1-2*x)*(1-4*x)*(1-6*x)*(1-8*x)).

E.g.f.: (-exp(2*x)+24*exp(4*x)-81*exp(6*x)+64*exp(8*x))/3!.