A330019 - OEIS

A330019

Expansion of e.g.f. 1 / (1 - Sum_{k>=1} binomial(k,floor(k/2)) * x^k / k!).

1, 1, 4, 21, 150, 1330, 14180, 176295, 2505230, 40049226, 711379872, 13899553206, 296270826852, 6841305568812, 170127212242416, 4532854743105975, 128824523061126750, 3890041395675793930, 124375112406132404960, 4197530354920789582410, 149118181703716510545260

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..20.

FORMULA

E.g.f.: 1 / (2 - BesselI(0,2*x) - BesselI(1,2*x)).

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * A001405(k) * a(n-k).

a(n) ~ n! / ((2 + BesselI(1, 2*r) + BesselI(2, 2*r)) * r^(n+1)), where r = 0.56298035651593906468222258870184730957829588917769... is the root of the equation BesselI(0,2*r) + BesselI(1,2*r) = 2. - Vaclav Kotesovec, Feb 09 2026

MATHEMATICA

nmax = 20; CoefficientList[Series[1/(2 - BesselI[0, 2 x] - BesselI[1, 2 x]), {x, 0, nmax}], x] Range[0, nmax]!

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] Binomial[k, Floor[k/2]] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}]

CROSSREFS

Cf. A001405, A054341, A305561, A308849, A328004.

Sequence in context: A346430 A324236 A392981 * A025164 A335848 A316370

Adjacent sequences: A330016 A330017 A330018 * A330020 A330021 A330022

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Nov 27 2019

STATUS

approved