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 A305561 Expansion of 2*x*(1 - 2*x)/(1 + 2*x - 8*x^2 - sqrt(1 - 4*x^2)). 0
 1, 1, 3, 8, 23, 64, 182, 512, 1451, 4096, 11594, 32768, 92710, 262144, 741548, 2097152, 5931955, 16777216, 47454210, 134217728, 379628818, 1073741824, 3037013748, 8589934592, 24296051198, 68719476736, 194368201572, 549755813888, 1554944869676, 4398046511104 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Invert transform of A001405. LINKS N. J. A. Sloane, Transforms Eric Weisstein's World of Mathematics, Central Binomial Coefficient FORMULA G.f.: 1/(1 - Sum_{k>=1} binomial(k,floor(k/2))*x^k). MAPLE a:= proc(n) option remember; `if`(n=0, 1, add(       a(n-i)*binomial(i, floor(i/2)), i=1..n))     end: seq(a(n), n=0..35);  # Alois P. Heinz, Jun 21 2018 MATHEMATICA nmax = 29; CoefficientList[Series[2 x (1 - 2 x)/(1 + 2 x - 8 x^2 - Sqrt[1 - 4 x^2]), {x, 0, nmax}], x] nmax = 29; CoefficientList[Series[1/(1 - Sum[Binomial[k, Floor[k/2]] x^k, {k, 1, nmax}]), {x, 0, nmax}], x] a[0] = 1; a[n_] := a[n] = Sum[Binomial[k, Floor[k/2]] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 29}] CROSSREFS Cf. A001405, A026671, A054341, A075436, A293732, A293741. Sequence in context: A316980 A017929 A017930 * A014398 A176880 A078054 Adjacent sequences:  A305558 A305559 A305560 * A305562 A305563 A305564 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Jun 21 2018 STATUS approved

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Last modified August 24 22:49 EDT 2019. Contains 326314 sequences. (Running on oeis4.)