A001781 Expansion of 1/((1+x)*(1-x)^10).

1, 9, 46, 174, 541, 1461, 3544, 7896, 16414, 32206, 60172, 107788, 186142, 311278, 505912, 801592, 1241383, 1883167, 2803658, 4103242, 5911763, 8395387, 11764688, 16284112, 22282988, 30168268, 40439192, 53704088, 70699532, 92312108, 119603024, 153835856, 196507709, 249384101

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (9,-35,75,-90,42,42,-90,75,-35,9,-1).

Crossrefs

Cf. A000582.

Tenth column of A112465.

Programs

Magma

[1/2903040*(2*n+11) *(2*n^8 +88*n^7 +1616*n^6 +16060*n^5 +93656*n^4 +324808*n^3 +646236*n^2 +663894*n +263655)+(-1)^n/1024  : n in [0..30]]; // Vincenzo Librandi, Oct 08 2011

Magma

R:=PowerSeriesRing(Integers(), 50);
Coefficients(R!( 1/((1+x)*(1-x)^10) )); // G. C. Greubel, Apr 20 2025

Maple

A001781 := proc(n) 1/2903040*(2*n+11) *(2*n^8 +88*n^7 +1616*n^6 +16060*n^5 +93656*n^4 +324808*n^3 +646236*n^2 +663894*n +263655)+(-1)^n/1024 ; end proc:
seq(A001781(n),n=0..50) ; # R. J. Mathar, Mar 22 2011

PARI

Vec(1/(1+x)/(1-x)^10+O(x^99)) \\ Charles R Greathouse IV, Apr 18 2012

SageMath

def A001781_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 1/((1+x)*(1-x)^10) ).list()
print(A001781_list(50)) # G. C. Greubel, Apr 20 2025

Formula

a(n) = +9*a(n-1) -35*a(n-2) +75*a(n-3) -90*a(n-4) +42*a(n-5) +42*a(n-6) -90*a(n-7) +75*a(n-8) -35*a(n-9) +9*a(n-10) -a(n-11). - R. J. Mathar, Mar 22 2011

a(n) + a(n+1) = A000582(n+10). - R. J. Mathar, Jan 06 2021