A330444 a(n) = Sum_{k=1..n} Stirling2(n,k) * (k-1)! * phi(k), where phi = A000010.

1, 2, 8, 44, 332, 2852, 28268, 330164, 4371452, 62867492, 980090828, 16792404884, 316446118172, 6484254233732, 142335512881388, 3299266086185204, 80092968046706492, 2040940536907449572, 55097942635383719948, 1586719679112182359124

Offset: 1

Author

Vaclav Kotesovec, Dec 15 2019

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..420

Crossrefs

Cf. A000010, A330351, A330353.

Programs

Mathematica

Table[Sum[StirlingS2[n, k] * (k-1)! * EulerPhi[k], {k, 1, n}], {n, 1, 20}]

PARI

a(n) = sum(k=1, n, stirling(n, k, 2)*(k-1)!*eulerphi(k)); \\ Michel Marcus, Dec 15 2019

Formula

a(n) ~ 3 * n! / (Pi^2 * (log(2))^(n+1)).