A370326 E.g.f.: exp(Sum_{k>=1} binomial(2*k,k) * x^k).

1, 2, 16, 200, 3376, 71552, 1822144, 54131072, 1836436480, 70016026112, 2962490758144, 137711245058048, 6974788150104064, 382232015239454720, 22531888624878813184, 1421482338801856053248, 95553266255536369893376, 6817598649041309962600448, 514534725049116493981941760

Offset: 0

Author

Vaclav Kotesovec, Feb 15 2024

Keywords

• nonn

Crossrefs

Cf. A000984, A065866, A213507, A251568, A370327.

Programs

Mathematica

CoefficientList[Series[Exp[Sum[Binomial[2*k,k]*x^k, {k, 1, 20}]], {x, 0, 20}], x] * Range[0, 20]!
CoefficientList[Series[Exp[1/Sqrt[1 - 4*x] - 1], {x, 0, 20}], x] * Range[0, 20]!

Formula

E.g.f.: exp(1/sqrt(1 - 4*x) - 1).

a(n) ~ exp(3*n^(1/3)/2^(2/3) - n - 1) * 2^(2*n + 1/6) * n^(n - 1/3) / sqrt(3).