A397013 - OEIS

%I #13 Jun 14 2026 18:30:58

%S 1,12,118,1152,11772,128160,1494576,18679680,249815520,3566142720,

%T 54187574400,873962127360,14920424467200,268923168460800,

%U 5104647388108800,101811581061120000,2129097359866982400,46590736318156800000,1064901291126220800000,25379394670728806400000

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

%H Paolo Xausa, <a href="/A397013/b397013.txt">Table of n, a(n) for n = 0..445</a>

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

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

%p prec := 20: egf := (1 - 23*z - (30 - 6*z)*log(1-z)) /(1 - z)^5:

%p ser := series(egf, z, prec+1): seq(n!*coeff(ser, z, n), n = 0..19);

%p # Alternative:

%p a := n -> (n + 3)! * ((n + 5) * harmonic(n + 3) - 3*n - 9):

%t A397013[n_] := (n + 3)!*((n + 5)*HarmonicNumber[n + 3] - 3*n - 9);

%t Array[A397013, 20, 0] (* _Paolo Xausa_, Jun 14 2026 *)

%Y Cf. A396981, A001008.

%K nonn

%O 0,2

%A _Peter Luschny_, Jun 14 2026