A163944 Fourth left hand column of triangle A163940.

0, 4, 49, 246, 834, 2250, 5214, 10829, 20696, 37044, 62875, 102124, 159834, 242346, 357504, 514875, 725984, 1004564, 1366821, 1831714, 2421250, 3160794, 4079394, 5210121, 6590424, 8262500, 10273679, 12676824, 15530746, 18900634, 22858500

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

G.f.: x*(4 +21*x -13*x^2 +x^3 +3*x^4 -x^5)/(1-x)^7.

a(n) = (10*n^2 +107*n^3 +61*n^4 +13*n^5 +n^6)/48.

a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7).

E.g.f.: (1/48)*x*(192 + 984*x + 888*x^2 + 256*x^3 + 28*x^4 + x^5)*exp(x). - G. C. Greubel, Aug 13 2017

Mathematica

CoefficientList[Series[x*(4 + 21*x - 13*x^2 + x^3 + 3*x^4 - x^5)/(1 - x)^7, {x, 0, 50}], x] (* G. C. Greubel, Aug 13 2017 *)
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 4, 49, 246, 834, 2250, 5214}, 40] (* Harvey P. Dale, Apr 29 2019 *)

Prog

(PARI) x='x+O('x^50); concat([0], Vec(x*(4 +21*x -13*x^2 +x^3 +3*x^4 -x^5)/(1-x)^7)) \\ G. C. Greubel, Aug 13 2017

Crossrefs

Cf. A163972.

Equals the fourth left hand column of A163940.

A163943 is another left hand column.

Sequence in context: A295535 A078187 A100256 * A000596 A113525 A290263

Adjacent sequences: A163941 A163942 A163943 * A163945 A163946 A163947

Keyword

easy,nonn

Author

Johannes W. Meijer, Aug 13 2009

Status

approved