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A376995 a(n) = floor(b(n)), where b(1) = 1 and b(n) = b(n-1) + Sum_{k=1..n-1} b(k)/(n-1).

%I A376995 #16 Oct 12 2024 11:18:54
%S A376995 1,2,3,5,8,12,18,25,35,48,64,85,111,143,184,234,296,371,463,575,709,
%T A376995 872,1066,1298,1575,1903,2293,2752,3294,3931,4677,5550,6570,7757,9138,
%U A376995 10741,12597,14744,17222,20078,23365,27141,31474,36438,42118,48607,56012,64451,74057
%N A376995 a(n) = floor(b(n)), where b(1) = 1 and b(n) = b(n-1) + Sum_{k=1..n-1} b(k)/(n-1).
%F A376995 a(n) = floor(b(n)), where b(n) = 2*b(n-1) - (1 - 1/(n-1))*b(n-2), b(1)=1, b(2)=2.
%F A376995 a(n) ~ exp(2*sqrt(n) - 1/2) / (2*sqrt(Pi)*n^(1/4)).
%F A376995 a(n) ~ exp(-1/2) * BesselI(0, 2*sqrt(n)).
%F A376995 a(n) = floor(A160617(n-1)/A160618(n-1)).
%t A376995 b[1]=1; b[n_]:=b[n] = b[n-1] + Sum[b[i], {i, 1, n-1}]/(n-1); Table[b[n], {n, 1, 50}] // Floor
%t A376995 Clear[b]; RecurrenceTable[{b[n] == 2*b[n-1] - (1-1/(n-1))*b[n-2], b[1]==1, b[2]==2}, b, {n, 1, 50}] // Floor
%t A376995 Table[HypergeometricPFQ[{n}, {1}, 1]/E, {n, 1, 50}] // Floor
%t A376995 Rest[CoefficientList[Series[x*E^(x/(1-x))/(1-x), {x, 0, 50}], x]] // Floor
%t A376995 nmax = 50; Rest[CoefficientList[Series[Integrate[Exp[t]*BesselI[0, 2*Sqrt[t]], {t, 0, x}], {x, 0, nmax}], x] * Range[0, nmax]!] // Floor
%t A376995 Table[LaguerreL[n-1, -1], {n, 1, 50}] // Floor
%Y A376995 Cf. A065094, A160617, A160618.
%K A376995 nonn
%O A376995 1,2
%A A376995 _Vaclav Kotesovec_, Oct 12 2024