A049017 Expansion of 1/((1-x)^7 - x^7).

1, 7, 28, 84, 210, 462, 924, 1717, 3017, 5110, 8568, 14756, 27132, 54264, 116281, 257775, 572264, 1246784, 2641366, 5430530, 10861060, 21242341, 40927033, 78354346, 150402700, 291693136, 574274008, 1148548016, 2326683921, 4749439975, 9714753412, 19818498700, 40199107690

Offset

0,2

Comments

Differs for n >= 7 (1717 vs. 1716) from A000579(n+6) = binomial(n+6,6); see also row 6 of A027555, A059481 and A213808. - M. F. Hasler, Mar 05 2017

Links

Seiichi Manyama, Table of n, a(n) for n = 0..3000

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,2).

Formula

G.f.: 1/((1-x)^7 - x^7) = 1/((1-2*x)*(1-5*x+11*x^2-13*x^3+9*x^4-3*x^5+x^6)).

Mathematica

CoefficientList[Series[1/((1-x)^7-x^7), {x, 0, 30}], x]  (* Harvey P. Dale, Feb 18 2011 *)

Prog

(PARI) Vec(1/((1-x)^7-x^7)+O(x^99)) \\ M. F. Hasler, Mar 05 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/((1-x)^7 - x^7) )); // G. C. Greubel, Apr 11 2023
(SageMath)
def A049017_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 1/((1-x)^7 - x^7) ).list()
A049017_list(40) # G. C. Greubel, Apr 11 2023

Crossrefs

Cf. A000579, A000750, A027555, A049018, A059481, A213808.

Sequences of the form 1/((1-x)^m - x^m): A000079 (m=1,2), A024495 (m=3), A000749 (m=4), A049016 (m=5), A192080 (m=6), this sequence (m=7), A290995 (m=8), A306939 (m=9).

Sequence in context: A278969 A000579 A290994 * A019501 A229887 A243741

Adjacent sequences: A049014 A049015 A049016 * A049018 A049019 A049020

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved