A277339 Exponential self-convolution of this sequence gives central binomial coefficients (A000984).

1, 1, 2, 4, 7, 11, 26, 92, 64, -1328, 2272, 86912, -157706, -7271042, 17815604, 853696664, -2615703541, -133125019397, 490820087366, 26636670621548, -114924854384183, -6653655394184683, 32904766004185814, 2029701686588972068, -11322597283993315976

Offset: 0

Author

Vladimir Reshetnikov, Oct 09 2016

Keywords

• sign

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..465

Crossrefs

Cf. A000984.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, (
      binomial(2*n, n)-add(a(k)*a(n-k)*
      binomial(n, k), k=1..n-1))/2)
    end:
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 12 2016

Mathematica

Table[SeriesCoefficient[Exp[x] Sqrt[BesselI[0, 2 x]], {x, 0, n}] n!, {n, 0, 25}]

PARI

x = 'x + O('x^30); serlaplace(exp(x)*sqrt(besseli(0, 2*x))) \\ Michel Marcus, Oct 09 2016

Formula

E.g.f.: exp(x)*sqrt(BesselI_0(2*x)).