A346846 E.g.f.: log(1 + x) / (1 - x)^4.

1, 7, 50, 386, 3304, 31176, 323280, 3656880, 44890560, 594463680, 8453128320, 128473430400, 2079045964800, 35692494566400, 648044312832000, 12406994498304000, 249834635947008000, 5278539223415808000, 116768100285720576000, 2699047267616544768000, 65071515565786447872000

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..445

Formula

a(n) = n! * Sum_{k=1..n} (-1)^(k+1) * binomial(n-k+3,3) / k.

a(n) ~ log(2) * n^3 * n! / 6. - Vaclav Kotesovec, Aug 06 2021

D-finite with recurrence: -(m - 2)*(m + 1)^2*a(m - 3) + (m^2 - 3*m - 6)*a(m - 2) + (m + 5)*a(m - 1) - a(m) = 0. - Robert Israel, Nov 18 2025

Maple

f:= proc(m) option remember;  -(m - 2)*(m + 1)^2*procname(m - 3) + (m^2 - 3*m - 6)*procname(m - 2) + (m + 5)*procname(m - 1) end proc:
f(0):= 0: f(1):= 1: f(2):= 7:
map(f, [$1..50]); # Robert Israel, Nov 18 2025

Mathematica

nmax = 21; CoefficientList[Series[Log[1 + x]/(1 - x)^4, {x, 0, nmax}], x] Range[0, nmax]! // Rest
Table[n! Sum[(-1)^(k + 1) Binomial[n - k + 3, 3]/k , {k, 1, n}], {n, 1, 21}]

Prog

(PARI) my(x='x+O('x^25)); Vec(serlaplace(log(1+x)/(1-x)^4)) \\ Michel Marcus, Aug 06 2021

Crossrefs

Cf. A000292, A001716, A024167, A109792, A346845, A346847.

Sequence in context: A081189 A108869 A065429 * A005460 A053155 A367235

Adjacent sequences: A346843 A346844 A346845 * A346847 A346848 A346849

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 05 2021

Status

approved