A397013 Expansion of the exponential generating function (1 - 23*x - (30 - 6*x)*log(1-x)) / (1 - x)^5.

1, 12, 118, 1152, 11772, 128160, 1494576, 18679680, 249815520, 3566142720, 54187574400, 873962127360, 14920424467200, 268923168460800, 5104647388108800, 101811581061120000, 2129097359866982400, 46590736318156800000, 1064901291126220800000, 25379394670728806400000

Offset

0,2

Links

Paolo Xausa, Table of n, a(n) for n = 0..445

Formula

a(n) = (n + 3)! * ((n + 5) * H(n + 3) - 3*n - 9), where H(n) is the n-th harmonic number.

a(n) = A396981(n, 12).

Maple

prec := 20: egf := (1 - 23*z - (30 - 6*z)*log(1-z)) /(1 - z)^5:
ser := series(egf, z, prec+1): seq(n!*coeff(ser, z, n), n = 0..19);
# Alternative:
a := n -> (n + 3)! * ((n + 5) * harmonic(n + 3) - 3*n - 9):

Mathematica

A397013[n_] := (n + 3)!*((n + 5)*HarmonicNumber[n + 3] - 3*n - 9);
Array[A397013, 20, 0] (* Paolo Xausa, Jun 14 2026 *)

Crossrefs

Cf. A396981, A001008.

Sequence in context: A016142 A105218 A180777 * A163950 A025132 A001712

Adjacent sequences: A397009 A397010 A397011 * A397014 A397015 A397016

Keyword

nonn

Author

Peter Luschny, Jun 14 2026

Status

approved