A000750 Expansion of bracket function. (Formerly M3851 N1576)

1, -5, 15, -35, 70, -125, 200, -275, 275, 0, -1000, 3625, -9500, 21250, -42500, 76875, -124375, 171875, -171875, 0, 621875, -2250000, 5890625, -13171875, 26343750, -47656250, 77109375, -106562500, 106562500, 0

Offset

0,2

Comments

It appears that the (unsigned) sequence is identical to its 5th-order absolute difference. - John W. Layman, Sep 23 2003

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

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

H. W. Gould, Binomial coefficients, the bracket function and compositions with relatively prime summands, Fib. Quart. 2(4) (1964), 241-260.

Index entries for linear recurrences with constant coefficients, signature (-5, -10, -10, -5).

Formula

G.f.: 1/((1+x)^5-x^5).

a(n) = (-1)^n * Sum_{k=0..floor(n/5)} (-1)^k * binomial(n+4,5*k+4). - Seiichi Manyama, Mar 21 2019

Mathematica

LinearRecurrence[{-5, -10, -10, -5}, {1, -5, 15, -35}, 30] (* Jean-François Alcover, Feb 11 2016 *)

Prog

(PARI) Vec(1/((1+x)^5-x^5) + O(x^40)) \\ Michel Marcus, Feb 11 2016
(PARI) {a(n) = (-1)^n*sum(k=0, n\5, (-1)^k*binomial(n+4, 5*k+4))} \\ Seiichi Manyama, Mar 21 2019

Crossrefs

Column 5 of A307047.

Cf. A000748, A000749, A001659, A006090, A049016.

Sequence in context: A292103 A290447 A360051 * A289389 A008487 A000743

Adjacent sequences: A000747 A000748 A000749 * A000751 A000752 A000753

Keyword

sign,easy

Author

N. J. A. Sloane

Status

approved