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

0,2

Links

Table of n, a(n) for n=0..22.

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

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}]

Prog

(PARI) a(n) = sum(k=0, n, binomial(n, k) * binomial(k, k\2) * 3^k); \\ Michel Marcus, Nov 21 2021

Crossrefs

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

Sequence in context: A275177 A079291 A173612 * A072221 A302064 A221849

Adjacent sequences: A349537 A349538 A349539 * A349541 A349542 A349543

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 21 2021

Status

approved