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 A171445 Sequence whose G.f is given by f(z)=(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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n)=2^(24)=16777216 for n>=24. We observe that this sequence is the transform of A171443 by the itered 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,...). REFERENCES Richard Choulet, Une nouvelle formule de combinatoire, Mathématique et Pédagogie, 157 (2006), 53-60. LINKS 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 *) CROSSREFS Cf. A040000, A113311, A115291, A171418, A171440, A171441, A171442, A171443. Sequence in context: A042206 A269448 A128377 * A264274 A278876 A053805 Adjacent sequences:  A171442 A171443 A171444 * A171446 A171447 A171448 KEYWORD easy,nonn AUTHOR Richard Choulet, Dec 09 2009 STATUS approved

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Last modified September 20 19:47 EDT 2021. Contains 347589 sequences. (Running on oeis4.)