A345102 a(n) = 1 + 3 * Sum_{k=0..n-1} binomial(n,k) * a(k) * a(n-k-1).

1, 4, 37, 589, 13276, 386059, 13741057, 578451514, 28109736811, 1548565036789, 95365652263102, 6492034471389889, 484086370908869821, 39238367740327468444, 3435176518078688461297, 323029539924876486293089, 32472511993953383052630556, 3475005417300807667690138399

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..343

Formula

E.g.f.: exp(x) / sqrt(7 - 6 * exp(x)).

Mathematica

a[n_] := a[n] = 1 + 3 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[7 - 6 Exp[x]], {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Sum[Binomial[n, k] StirlingS2[k, j] 3^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(7-6*exp(x)))) \\ Seiichi Manyama, Oct 20 2021

Crossrefs

Cf. A006677, A011781, A052886, A201354, A345103.

Sequence in context: A185082 A377741 A259822 * A036245 A133471 A249607

Adjacent sequences: A345099 A345100 A345101 * A345103 A345104 A345105

Keyword

nonn

Author

Ilya Gutkovskiy, Jun 08 2021

Status

approved