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

0,3

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).

Formula

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

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

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 *)

Prog

(PARI) my(x='x+O('x^30)); concat([0], Vec(x*(1-x)^7/(1-2*x)^8)) \\ G. C. Greubel, Jan 16 2020
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); [0] cat Coefficients(R!( x*(1-x)^7/(1-2*x)^8 )); // G. C. Greubel, Jan 16 2020
(Sage)
def A055854_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( x*(1-x)^7/(1-2*x)^8 ).list()
A055854_list(30) # G. C. Greubel, Jan 16 2020

Crossrefs

Cf. A011782, A049600, A055587, A055853.

Sequence in context: A197499 A036425 A126085 * A202514 A005025 A122588

Adjacent sequences: A055851 A055852 A055853 * A055855 A055856 A055857

Keyword

nonn,easy

Author

Wolfdieter Lang May 30 2000

Status

approved