A134377 Binomial transform of A045621.

1, 3, 10, 32, 101, 315, 975, 3001, 9199, 28109, 85680, 260650, 791663, 2401313, 7275738, 22024152, 66615351, 201349365, 608227698, 1836345996, 5541690723, 16716767709, 50408518791, 151954553565, 457926628077, 1379630558935, 4155518092780, 12513892232666, 37676692203405

Offset: 1

Author

Gary W. Adamson, Oct 22 2007

Keywords

• nonn

Comments

Given A045621 starting (1, 2, 5, 10, 22, 44, 93, ...).

Note that this uses an incorrect offset of -1 with A045621. - R. J. Mathar, Apr 04 2012

Examples

			a(4) = 32 = (1, 3, 3, 1) dot (1, 2, 5, 10) = (1 + 6 + 15 + 10).
		

Crossrefs

Cf. A007318, A045621.

Programs

Mathematica

s[n_] := 2^n - Binomial[n, Floor[n/2]]; Table[Sum[Binomial[n, k]*s[k + 1], {k, 0, n}], {n, 0, 28}] (* Amiram Eldar, May 31 2025 *)

Formula

A007318 * A045621, A045621 starting with 1.

Extensions

More terms from Amiram Eldar, May 31 2025