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

Author

Johannes W. Meijer, Aug 13 2009

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A163972.

Equals the fourth left hand column of A163940.

A163943 is another left hand column.

Programs

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 *)

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

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