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 A345103 a(n) = 1 + 4 * Sum_{k=0..n-1} binomial(n,k) * a(k) * a(n-k-1). 2
 1, 5, 61, 1277, 37741, 1437725, 67013101, 3693540317, 234974905261, 16945434018845, 1366008048556141, 121721015465713757, 11880107754103150381, 1260413749895624939165, 144427420001275864755181, 17776090894283922227621597, 2338833689096321086977341101, 327585830473259220341296486685 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..331 FORMULA E.g.f.: exp(x) / sqrt(9 - 8 * exp(x)). MATHEMATICA a[n_] := a[n] = 1 + 4 Sum[Binomial[n, k] a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 17}] nmax = 17; CoefficientList[Series[Exp[x]/Sqrt[9 - 8 Exp[x]], {x, 0, nmax}], x] Range[0, nmax]! Table[Sum[Sum[Binomial[n, k] StirlingS2[k, j] 4^j (2 j - 1)!!, {j, 0, k}], {k, 0, n}], {n, 0, 17}] PROG (PARI) N=20; x='x+O('x^N); Vec(serlaplace(exp(x)/sqrt(9-8*exp(x)))) \\ Seiichi Manyama, Oct 20 2021 CROSSREFS Cf. A006677, A052886, A144828, A201365, A345102. Sequence in context: A009825 A065919 A196125 * A096537 A115047 A000364 Adjacent sequences: A345100 A345101 A345102 * A345104 A345105 A345106 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Jun 08 2021 STATUS approved

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Last modified September 24 12:17 EDT 2023. Contains 365579 sequences. (Running on oeis4.)