cp's OEIS Frontend

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

%I A277339 #9 Oct 12 2016 19:23:43
%S A277339 1,1,2,4,7,11,26,92,64,-1328,2272,86912,-157706,-7271042,17815604,
%T A277339 853696664,-2615703541,-133125019397,490820087366,26636670621548,
%U A277339 -114924854384183,-6653655394184683,32904766004185814,2029701686588972068,-11322597283993315976
%N A277339 Exponential self-convolution of this sequence gives central binomial coefficients (A000984).
%H A277339 Alois P. Heinz, <a href="/A277339/b277339.txt">Table of n, a(n) for n = 0..465</a>
%F A277339 E.g.f.: exp(x)*sqrt(BesselI_0(2*x)).
%p A277339 a:= proc(n) option remember; `if`(n=0, 1, (
%p A277339       binomial(2*n, n)-add(a(k)*a(n-k)*
%p A277339       binomial(n, k), k=1..n-1))/2)
%p A277339     end:
%p A277339 seq(a(n), n=0..25);  # _Alois P. Heinz_, Oct 12 2016
%t A277339 Table[SeriesCoefficient[Exp[x] Sqrt[BesselI[0, 2 x]], {x, 0, n}] n!, {n, 0, 25}]
%o A277339 (PARI) x = 'x + O('x^30); serlaplace(exp(x)*sqrt(besseli(0, 2*x))) \\ _Michel Marcus_, Oct 09 2016
%Y A277339 Cf. A000984.
%K A277339 sign
%O A277339 0,3
%A A277339 _Vladimir Reshetnikov_, Oct 09 2016