A055854 Convolution of A055853 with A011782.

0, 1, 9, 53, 253, 1059, 4043, 14407, 48639, 157184, 489872, 1480608, 4358752, 12541184, 35364864, 97960192, 267050240, 717619200, 1903452160, 4989337600, 12937052160, 33212530688, 84484882432, 213090238464, 533236219904

Offset: 0

Author

Wolfdieter Lang May 30 2000

Keywords

• nonn
• easy

Comments

Ninth column of triangle A055587.

T(n,7) of array T as in A049600.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (16,-112,448,-1120,1792,-1792,1024,-256).

Crossrefs

Cf. A011782, A049600, A055587, A055853.

Programs

Magma

R:=PowerSeriesRing(Integers(), 30); [0] cat Coefficients(R!( x*(1-x)^7/(1-2*x)^8 )); // G. C. Greubel, Jan 16 2020

Maple

seq(coeff(series(x*(1-x)^7/(1-2*x)^8, x, n+1), x, n), n = 0..30); # G. C. Greubel, Jan 16 2020

Mathematica

CoefficientList[Series[x*(1-x)^7/(1-2*x)^8, {x,0,30}], x] (* G. C. Greubel, Jan 16 2020 *)
LinearRecurrence[{16,-112,448,-1120,1792,-1792,1024,-256},{0,1,9,53,253,1059,4043,14407,48639,157184},40] (* Harvey P. Dale, Nov 04 2023 *)

PARI

my(x='x+O('x^30)); concat([0], Vec(x*(1-x)^7/(1-2*x)^8)) \\ G. C. Greubel, Jan 16 2020

Sage

def A055854_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( x*(1-x)^7/(1-2*x)^8 ).list()
A055854_list(30) # G. C. Greubel, Jan 16 2020

Formula

a(n)= T(n, 7)= A055587(n+7, 8).

G.f.: x*(1-x)^7/(1-2*x)^8.