A055852 Convolution of A055589 with A011782.

0, 1, 7, 34, 138, 501, 1683, 5336, 16172, 47264, 134048, 370688, 1003136, 2664192, 6960384, 17922048, 45552640, 114442240, 284508160, 700579840, 1710161920, 4141416448, 9955639296, 23770693632, 56400543744, 133041225728

Offset: 0

Author

Wolfdieter Lang May 30 2000

Keywords

• nonn
• easy

Comments

Seventh column of triangle A055587.

T(n,5) 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 (12,-60,160,-240,192,-64).

Crossrefs

Cf. A011782, A049600, A055587, A055589.

Programs

GAP

a:=[1,7,34,138,501,1683];; for n in [7..30] do a[n]:=12*a[n-1] -60*a[n-2] +160*a[n-3] -240*a[n-4] +192*a[n-5] -64*a[n-6]; od; Concatenation([0], a); # G. C. Greubel, Jan 16 2020

Magma

R:=PowerSeriesRing(Integers(), 30); [0] cat Coefficients(R!( x*(1-x)^5/(1-2*x)^6 )); // G. C. Greubel, Jan 16 2020

Maple

seq(coeff(series(x*(1-x)^5/(1-2*x)^6, x, n+1), x, n), n = 0..30); # G. C. Greubel, Jan 16 2020

Mathematica

CoefficientList[Series[x*(1-x)^5/(1-2*x)^6, {x,0,30}], x] (* G. C. Greubel, Jan 16 2020 *)

PARI

my(x='x+O('x^30)); concat([0], Vec(x*(1-x)^5/(1-2*x)^6)) \\ G. C. Greubel, Jan 16 2020

Sage

def A055852_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( x*(1-x)^5/(1-2*x)^6 ).list()
A055852_list(30) # G. C. Greubel, Jan 16 2020

Formula

a(n) = T(n, 5) = A055587(n+5, 6).

G.f.: x*(1-x)^5/(1-2*x)^6.