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A277339
Exponential self-convolution of this sequence gives central binomial coefficients (A000984).
1
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
0,3
LINKS
FORMULA
E.g.f.: exp(x)*sqrt(BesselI_0(2*x)).
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}]
PROG
(PARI) x = 'x + O('x^30); serlaplace(exp(x)*sqrt(besseli(0, 2*x))) \\ Michel Marcus, Oct 09 2016
CROSSREFS
Cf. A000984.
Sequence in context: A360886 A304040 A261145 * A153555 A259588 A058103
KEYWORD
sign
AUTHOR
STATUS
approved