A140227 Binomial transform of [1, 4, 6, 4, 1, 1, -1, 1, -1, 1, ...].

1, 5, 15, 35, 70, 127, 215, 345, 530, 785, 1127, 1575, 2150, 2875, 3775, 4877, 6210, 7805, 9695, 11915, 14502, 17495, 20935, 24865, 29330, 34377, 40055, 46415, 53510, 61395, 70127, 79765, 90370, 102005, 114735, 128627, 143750, 160175, 177975

Offset

1,2

Links

Table of n, a(n) for n=1..39.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

A007318 * [1, 4, 6, 4, 1, 1, -1, 1, -1, 1, ...].

From R. J. Mathar, Jun 18 2008: (Start)

O.g.f.: x*(1+x)*(x^4 - x^3 + x^2 - x + 1)/(1-x)^5.

a(n) = 2 + 35*(n-1)^2/12 + (n-1)^4/12, n > 1. (End)

Example

a(4) = 35 = (1, 3, 3, 1) dot (1, 4, 6, 4) = (1 + 12 + 18 + 4).

Mathematica

CoefficientList[Series[x(1+x)(x^4-x^3+x^2-x+1)/(1-x)^5, {x, 0, 40}], x] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {0, 1, 5, 15, 35, 70, 127}, 50] (* Harvey P. Dale, Mar 11 2023 *)

Crossrefs

Sequence in context: A000332 A342213 A373936 * A264925 A049016 A139761

Adjacent sequences: A140224 A140225 A140226 * A140228 A140229 A140230

Keyword

nonn

Author

Gary W. Adamson, May 12 2008

Extensions

More terms from R. J. Mathar, Jun 18 2008

Status

approved