A035028 First differences of A002002.

4, 20, 104, 552, 2972, 16172, 88720, 489872, 2719028, 15157188, 84799992, 475894200, 2677788492, 15102309468, 85347160608, 483183316512, 2739851422820, 15558315261812, 88462135512712, 503569008273992, 2869602773253884, 16368396446913420, 93449566652932784

Offset

0,1

Links

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

Formula

a(n) = A049600(n, n-3).

D-finite with recurrence: (n+2)*a(n) - (7*n+8)*a(n-1) + (7*n-8)*a(n-2) - (n-2)*a(n-3) = 0. - R. J. Mathar, Jan 28 2020

a(n) = ((n+1)*(n+3)*A001850(n+3) - (6*n^2 +22*n +17)*A001850(n+2) + (n+2)*(5*n+8)*A001850(n+1))/(2*(n+1)*(n+2)), A001850(n) = LegrndreP(n, 3). - G. C. Greubel, Oct 19 2022

Mathematica

Differences[CoefficientList[Series[((1-x)/Sqrt[1-6x+x^2]-1)/2, {x, 0, 30}], x]] (* Harvey P. Dale, Jun 04 2011 *)
With[{P=LegendreP}, Table[(n*(n+2)*P[n+2, 3] -(6*n^2+10*n+1)*P[n+1, 3] +(n+1)*(5*n+ 3)*P[n, 3])/(2*n*(n+1)), {n, 30}]] (* G. C. Greubel, Oct 19 2022 *)

Prog

(Magma) I:=[4, 20, 104]; [n le 3 select I[n] else ( (7*n+1)*Self(n-1) - (7*n-15)*Self(n-2) + (n-3)*Self(n-3) )/(n+1): n in [1..30]]; // G. C. Greubel, Oct 19 2022
(SageMath)
def A001850(n): return gen_legendre_P(n, 0, 3)
def A035028(n): return ((n+1)*(n+3)*A001850(n+3) - (6*n^2 +22*n +17)*A001850(n+2) + (n+2)*(5*n+8)*A001850(n+1))/(2*(n+1)*(n+2))
[A035028(n) for n in range(40)] # G. C. Greubel, Oct 19 2022

Crossrefs

Cf. A001850, A002002, A035029, A049600.

Sequence in context: A082761 A076035 A120978 * A104550 A089382 A291089

Adjacent sequences: A035025 A035026 A035027 * A035029 A035030 A035031

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Harvey P. Dale, Jun 04 2011

Status

approved