A128499 Fifth column (m=4) of triangle A128494.

1, 1, -4, -4, 11, 11, -24, -24, 46, 46, -80, -80, 130, 130, -200, -200, 295, 295, -420, -420, 581, 581, -784, -784, 1036, 1036, -1344, -1344, 1716, 1716, -2160, -2160, 2685, 2685, -3300, -3300, 4015, 4015, -4840, -4840, 5786, 5786, -6864, -6864, 8086, 8086, -9464, -9464, 11011, 11011, -12740

Offset: 0

Author

Wolfdieter Lang, Apr 04 2007

Keywords

• sign
• easy

Comments

Unsigned, this is the repeated sequence A001752.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,-5,5,-10,10,-10,10,-5,5,-1,1).

Crossrefs

Cf. A128498 (column m=3).

Programs

Mathematica

LinearRecurrence[{1,-5,5,-10,10,-10,10,-5,5,-1,1},{1,1,-4,-4,11,11,-24,-24,46,46,-80},60] (* Harvey P. Dale, Aug 26 2023 *)

PARI

Vec(-1/((x-1)*(x^2+1)^5) + O(x^100)) \\ Colin Barker, Mar 14 2015

Formula

G.f.: -1 / ((x-1)*(x^2+1)^5). - Corrected by Colin Barker, Mar 14 2015

a(2*k) = a(2*k+1) = ((-1)^k)*A001752(n), k>=0.

a(n) = ((2*n^4+44*n^3+334*n^2+1012*n+993)*(-1)^((2*n-1+(-1)^n)/4)+(4*n^3+66*n^2+332*n+495)*(-1)^((6*n-1+(-1)^n)/4)+48)/1536. - Luce ETIENNE, Mar 14 2015