A373175 - OEIS

%I #11 May 27 2024 15:48:45

%S 1,3,8,25,87,386,1663,11313,39560,717067,-2408199,128675438,

%T -2009225567,53624676795,-1282589050168,35660396328721,

%U -1032462831852297,32302377782200418,-1070227545188815745,37651172275242136857,-1398665563931458389304,54757245858874447661683

%N Expansion of e.g.f. exp(sqrt(2*x+1)-1)/(2-sqrt(2*x+1))^2.

%H Y. Alp and E. G. Kocer, <a href="https://doi.org/10.1007/s00025-024-02193-5">Exponential Almost-Riordan Arrays</a>, Results Math 79, 173 (2024). See page 24.

%t a[n_]:=n!SeriesCoefficient[Exp[Sqrt[2x+1]-1]/(2-Sqrt[2x+1])^2,{x,0,n}]; Array[a,22,0]

%o (PARI) my(x = 'x+O('x^30)); Vec(serlaplace(exp(sqrt(2*x+1)-1)/(2-sqrt(2*x+1))^2)) \\ _Michel Marcus_, May 27 2024

%Y Cf. A000806, A330797, A373176.

%K sign

%O 0,2

%A _Stefano Spezia_, May 26 2024