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 A355109 a(n) = 1 + Sum_{k=1..n-1} binomial(n-1,k) * 2^(k-1) * a(k). 0
 1, 1, 2, 7, 44, 493, 9974, 372403, 26247008, 3559692121, 942403603562, 491777568765151, 508938530329020692, 1048381120745440503877, 4307758467916752367544414, 35349370769806113877653011083, 579693879415731511179957972407624 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..16. FORMULA G.f. A(x) satisfies: A(x) = (2 - x + x * A(2*x/(1 - x))) / (2 * (1 - x)). MAPLE a:= proc(n) option remember; 1+add(a(k)* binomial(n-1, k)*2^(k-1), k=1..n-1) end: seq(a(n), n=0..16); # Alois P. Heinz, Jun 19 2022 MATHEMATICA a[n_] := a[n] = 1 + Sum[Binomial[n - 1, k] 2^(k - 1) a[k], {k, 1, n - 1}]; Table[a[n], {n, 0, 16}] nmax = 16; A[_] = 0; Do[A[x_] = (2 - x + x A[2 x/(1 - x)])/(2 (1 - x)) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] CROSSREFS Cf. A000110, A126443, A352859, A352860. Sequence in context: A348857 A172389 A153522 * A278295 A356613 A107354 Adjacent sequences: A355106 A355107 A355108 * A355110 A355111 A355112 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Jun 19 2022 STATUS approved

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Last modified May 19 08:13 EDT 2024. Contains 372666 sequences. (Running on oeis4.)