A171445 Expansion of g.f. (1+z)^(24)/(1-z).

1, 25, 301, 2325, 12951, 55455, 190051, 536155, 1271626, 2579130, 4540386, 7036530, 9740686, 12236830, 14198086, 15505590, 16241061, 16587165, 16721761, 16764265, 16774891, 16776915, 16777191, 16777215, 16777216, 16777216

Offset: 0

Author

Richard Choulet, Dec 09 2009

Keywords

• easy
• nonn

Comments

a(n)=2^(24)=16777216 for n>=24. We observe that this sequence is the transform of A171443 by the iterated T^(16) of T such that: T(u_0,u_1,u_2,u_3,u_4,u_5,...)=(u_0,u_0+u_1,u_1+u_2,u_2+u_3,u_3+u_4,...).

Examples

			a(3) = C(25,3)+C(25,3-2) = 2325.
		

Links

• Richard Choulet, Une nouvelle formule de combinatoire?, Mathématique et Pédagogie, 157 (2006), p. 53-60. In French.
• Index entries for linear recurrences with constant coefficients, signature (1).

Crossrefs

Cf. A040000, A113311, A115291, A171418, A171440, A171441, A171442, A171443.

Programs

Maple

m:=25:for n from 0 to 40 do a(n):=sum('binomial(m,n-2*k)',k=0..floor(n/2)): od : seq(a(n),n=0..40);

Mathematica

CoefficientList[Series[(1+x)^24/(1-x),{x,0,30}],x] (* Harvey P. Dale, Jun 11 2019 *)

Formula

With m=25, a(n) = Sum_{k=0..floor(n/2)} binomial(m,n-2*k).