A365106 Sum_{n>=0} a(n) * x^n / n!^2 = exp( Sum_{n>=1} prime(n) * x^n / n!^2 ).

1, 2, 11, 107, 1577, 32201, 860460, 28921567, 1187475909, 58232016701, 3350187053856, 222857979706305, 16935374386652282, 1455271176236200143, 140181486948923188907, 15023106134895469195114, 1779460642743292348315607, 231607462899834684300774917, 32954119475274480307491604062, 5102159139278049158548905019487

Offset: 0

Author

Ilya Gutkovskiy, Aug 21 2023

Keywords

• nonn

Crossrefs

Cf. A007446, A023998.

Programs

Mathematica

nmax = 19; CoefficientList[Series[Exp[Sum[Prime[k] x^k/k!^2, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!^2
a[0] = 1; a[n_] := a[n] = (1/n) Sum[Binomial[n, k]^2 k Prime[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 19}]

Formula

a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} binomial(n,k)^2 * k * prime(k) * a(n-k).