A349540 - OEIS

%I #9 Nov 26 2021 05:17:54

%S 1,4,25,145,931,5866,38359,249880,1655035,10968724,73320259,491001721,

%T 3304488565,22283168350,150744668065,1021597533865,6938921001235,

%U 47202858834100,321640950882475,2194500145215595,14992297096036345,102535471011848230,702004865920831525

%N E.g.f.: exp(x) * (BesselI(0,6*x) + BesselI(1,6*x)).

%F a(n) = Sum_{k=0..n} binomial(n,k) * binomial(k,floor(k/2)) * 3^k.

%F a(n) ~ 7^(n + 1/2) / sqrt(3*Pi*n). - _Vaclav Kotesovec_, Nov 26 2021

%t nmax = 22; CoefficientList[Series[Exp[x] (BesselI[0, 6 x] + BesselI[1, 6 x]), {x, 0, nmax}], x] Range[0, nmax]!

%t Table[Sum[Binomial[n, k] Binomial[k, Floor[k/2]] 3^k, {k, 0, n}], {n, 0, 22}]

%o (PARI) a(n) = sum(k=0, n, binomial(n,k) * binomial(k, k\2) * 3^k); \\ _Michel Marcus_, Nov 21 2021

%Y Cf. A001405, A005773, A026378, A151318, A349541.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Nov 21 2021