A001808 Expansion of 1/((1+x)*(1-x)^12).

1, 11, 67, 297, 1068, 3300, 9076, 22748, 52834, 115126, 237590, 467842, 884236, 1611908, 2845492, 4880668, 8157227, 13316953, 21280337, 33346963, 51325352, 77699128, 115837592, 170260168, 246965732, 353839564, 501152588, 702169700, 973886344, 1337915096

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (11,-54,154,-275,297,-132,-132,297,-275,154,-54,11,-1).

Crossrefs

Twelfth column of A112465.

Programs

Magma

R:=PowerSeriesRing(Integers(), 50);
Coefficients(R!( 1/((1+x)*(1-x)^12) )); // G. C. Greubel, Apr 20 2025

Mathematica

CoefficientList[Series[1/((1+x)(1-x)^12),{x,0,50}],x] (* Vincenzo Librandi, Feb 24 2012 *)
LinearRecurrence[{11,-54,154,-275,297,-132,-132,297,-275,154,-54,11,-1},{1,11,67,297,1068,3300,9076,22748,52834,115126,237590,467842,884236},30] (* Harvey P. Dale, Jun 22 2014 *)

PARI

Vec(1/((1+x)*(1-x)^12)+O(x^20)) \\ Edward Jiang, Sep 07 2014

SageMath

def A001808_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 1/((1+x)*(1-x)^12) ).list()
print(A001808_list(50)) # G. C. Greubel, Apr 20 2025