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A171445
Expansion of g.f. (1+z)^(24)/(1-z).
0
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
0,2
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,...).
LINKS
Richard Choulet, Une nouvelle formule de combinatoire?, Mathématique et Pédagogie, 157 (2006), p. 53-60. In French.
FORMULA
With m=25, a(n) = Sum_{k=0..floor(n/2)} binomial(m,n-2*k).
EXAMPLE
a(3) = C(25,3)+C(25,3-2) = 2325.
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 *)
KEYWORD
easy,nonn
AUTHOR
Richard Choulet, Dec 09 2009
STATUS
approved