This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A380308 #18 Jan 21 2025 05:00:06
%S A380308 1,-1,-2,-7,-35,-226,-1769,-16003,-159998,-1669645,-16203509,
%T A380308 -85724926,2606965153,154547040023,6047755681150,217270016433329,
%U A380308 7721994442008061,279057037146008702,10378357435103977207,399487271346562859045,15957215240554330744066
%N A380308 Expansion of e.g.f. exp( 1 - 1/(1-2*x)^(1/2) ).
%H A380308 Seiichi Manyama, <a href="/A380308/b380308.txt">Table of n, a(n) for n = 0..405</a>
%F A380308 a(n) = Sum_{k=0..n} 2^(n-k) * |Stirling1(n,k)| * A000587(k).
%F A380308 a(n) = e * (-2)^n * n! * Sum_{k>=0} (-1)^k * binomial(-k/2,n)/k!.
%F A380308 a(0) = 1; a(n) = -Sum_{k=1..n} A001147(k) * binomial(n-1,k-1) * a(n-k).
%o A380308 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(1-1/(1-2*x)^(1/2))))
%Y A380308 Cf. A145561, A380309, A380310.
%Y A380308 Cf. A000587, A001147.
%K A380308 sign
%O A380308 0,3
%A A380308 _Seiichi Manyama_, Jan 20 2025