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).

1, 2, 3, 5, 8, 12, 18, 25, 35, 48, 64, 85, 111, 143, 184, 234, 296, 371, 463, 575, 709, 872, 1066, 1298, 1575, 1903, 2293, 2752, 3294, 3931, 4677, 5550, 6570, 7757, 9138, 10741, 12597, 14744, 17222, 20078, 23365, 27141, 31474, 36438, 42118, 48607, 56012, 64451, 74057

Offset: 1

Author

Vaclav Kotesovec, Oct 12 2024

Keywords

• nonn

Crossrefs

Cf. A065094, A160617, A160618.

Programs

Mathematica

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
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
Table[HypergeometricPFQ[{n}, {1}, 1]/E, {n, 1, 50}] // Floor
Rest[CoefficientList[Series[x*E^(x/(1-x))/(1-x), {x, 0, 50}], x]] // Floor
nmax = 50; Rest[CoefficientList[Series[Integrate[Exp[t]*BesselI[0, 2*Sqrt[t]], {t, 0, x}], {x, 0, nmax}], x] * Range[0, nmax]!] // Floor
Table[LaguerreL[n-1, -1], {n, 1, 50}] // Floor

Formula

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.

a(n) ~ exp(2*sqrt(n) - 1/2) / (2*sqrt(Pi)*n^(1/4)).

a(n) ~ exp(-1/2) * BesselI(0, 2*sqrt(n)).

a(n) = floor(A160617(n-1)/A160618(n-1)).