A349541 E.g.f.: exp(x) * (BesselI(0,8*x) + BesselI(1,8*x)).

1, 5, 41, 301, 2513, 20181, 170745, 1423101, 12161441, 103344037, 889924553, 7650373325, 66271512433, 574065261173, 4996181205657, 43511277885597, 380108373809985, 3323551100483397, 29122753514303337, 255427680480306285, 2243831648555990289, 19728657265135701525

Offset: 0

Author

Ilya Gutkovskiy, Nov 21 2021

Keywords

• nonn

Crossrefs

Cf. A001405, A005573, A005773, A151318, A349540.

Programs

Mathematica

nmax = 21; CoefficientList[Series[Exp[x] (BesselI[0, 8 x] + BesselI[1, 8 x]), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Binomial[n, k] Binomial[k, Floor[k/2]] 4^k, {k, 0, n}], {n, 0, 21}]

PARI

a(n) = sum(k=0, n, binomial(n,k) * binomial(k, k\2) * 4^k); \\ Michel Marcus, Nov 21 2021

Formula

a(n) = Sum_{k=0..n} binomial(n,k) * binomial(k,floor(k/2)) * 4^k.

a(n) ~ 3^(2*n + 1) / (2*sqrt(Pi*n)). - Vaclav Kotesovec, Nov 26 2021