A349540 E.g.f.: exp(x) * (BesselI(0,6*x) + BesselI(1,6*x)).
1, 4, 25, 145, 931, 5866, 38359, 249880, 1655035, 10968724, 73320259, 491001721, 3304488565, 22283168350, 150744668065, 1021597533865, 6938921001235, 47202858834100, 321640950882475, 2194500145215595, 14992297096036345, 102535471011848230, 702004865920831525
Offset: 0
Keywords
Programs
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Mathematica
nmax = 22; CoefficientList[Series[Exp[x] (BesselI[0, 6 x] + BesselI[1, 6 x]), {x, 0, nmax}], x] Range[0, nmax]! Table[Sum[Binomial[n, k] Binomial[k, Floor[k/2]] 3^k, {k, 0, n}], {n, 0, 22}] -
PARI
a(n) = sum(k=0, n, binomial(n,k) * binomial(k, k\2) * 3^k); \\ Michel Marcus, Nov 21 2021
Formula
a(n) = Sum_{k=0..n} binomial(n,k) * binomial(k,floor(k/2)) * 3^k.
a(n) ~ 7^(n + 1/2) / sqrt(3*Pi*n). - Vaclav Kotesovec, Nov 26 2021