A140228 Binomial transform of [1, 5, 10, 10, 5, 1, 1, -1, 1, -1, 1, ...].

1, 6, 21, 56, 126, 252, 463, 798, 1308, 2058, 3129, 4620, 6650, 9360, 12915, 17506, 23352, 30702, 39837, 51072, 64758, 81284, 101079, 124614, 152404, 185010, 223041, 267156, 318066, 376536, 443387

Offset

0,2

Links

Table of n, a(n) for n=0..30.

Formula

A007318 * [1, 5, 10, 10, 5, 1, 1, -1, 1, -1, 1, ...]

From Emeric Deutsch, Jun 03 2008: (Start)

a(n) = n*(274 + 85*n + n^4)/60 for n >= 1.

G.f.: (1+x^6)/(1-x)^6. (End)

Example

a(4) = 56 = (1, 3, 3, 1) dot (1, 5, 10, 10) = (1 + 15 + 30 + 10).

Maple

1, seq((1/60)*n*(274+85*n^2+n^4), n=1..30); # Emeric Deutsch, Jun 03 2008

Crossrefs

Cf. A007318.

Sequence in context: A090581 A000389 A143980 * A264926 A006090 A192080

Adjacent sequences: A140225 A140226 A140227 * A140229 A140230 A140231

Keyword

nonn

Author

Gary W. Adamson, May 12 2008

Extensions

More terms from Emeric Deutsch, Jun 03 2008

Status

approved