A308847 Expansion of e.g.f. exp(-2*x) / BesselI(0,2*x).

1, -2, 2, 4, -14, -52, 284, 1496, -10958, -74372, 681652, 5656616, -62226116, -610306712, 7832965352, 88645228304, -1300254163918, -16676932459172, 275196007522436, 3944890321174664, -72330003541955564, -1145979961718846152, 23112838345877865752, 401070175407076000624, -8824400094691629670724

Offset

0,2

Comments

E.g.f. is inverse of e.g.f. for A000984 (central binomial coefficients).

Links

Table of n, a(n) for n=0..24.

Formula

E.g.f.: 1 / Sum_{k>=0} binomial(2*k,k)*x^k/k!.

Mathematica

nmax = 24; CoefficientList[Series[Exp[-2 x]/BesselI[0, 2 x], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = -Sum[Binomial[n, k] Binomial[2 k, k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 24}]

Prog

(PARI) my(x='x+O('x^30)); Vec(serlaplace(exp(-2*x) / besseli(0, 2*x))) \\ Michel Marcus, Jul 02 2019

Crossrefs

Cf. A000984, A002420, A178955, A308848.

Sequence in context: A019072 A019073 A153959 * A006205 A360194 A268073

Adjacent sequences: A308844 A308845 A308846 * A308848 A308849 A308850

Keyword

sign

Author

Ilya Gutkovskiy, Jun 28 2019

Status

approved