A346847 E.g.f.: log(1 + x) / (1 - x)^5.

1, 9, 77, 694, 6774, 71820, 826020, 10265040, 137275920, 1967222880, 30092580000, 489584390400, 8443643040000, 153903497126400, 2956596769728000, 59712542813952000, 1264947863784192000, 28047600771531264000, 649672514944814592000, 15692497566512836608000, 394613964462556016640000

Offset: 1

Author

Ilya Gutkovskiy, Aug 05 2021

Keywords

• nonn

Crossrefs

Cf. A000332, A001721, A024167, A109792, A346845, A346846.

Programs

Mathematica

nmax = 21; CoefficientList[Series[Log[1 + x]/(1 - x)^5, {x, 0, nmax}], x] Range[0, nmax]! // Rest
Table[n! Sum[(-1)^(k + 1) Binomial[n - k + 4, 4]/k , {k, 1, n}], {n, 1, 21}]

PARI

my(x='x+O('x^25)); Vec(serlaplace(log(1+x)/(1-x)^5)) \\ Michel Marcus, Aug 06 2021

Formula

a(n) = n! * Sum_{k=1..n} (-1)^(k+1) * binomial(n-k+4,4) / k.

a(n) ~ log(2) * n^4 * n! / 24. - Vaclav Kotesovec, Aug 06 2021