A346946 Expansion of e.g.f. log( 1 + log(1 + x)^4 / 4! ).

1, -10, 85, -735, 6734, -66024, 693230, -7774250, 92759821, -1172483598, 15630569591, -218793782025, 3201481037819, -48746860400024, 768683653934928, -12487871805640344, 207761719406853466, -3513910668343842900, 59833161662103132050, -1011244718827893629750

Offset

4,2

Links

Table of n, a(n) for n=4..23.

Formula

a(n) = Stirling1(n,4) - (1/n) * Sum_{k=1..n-1} binomial(n,k) * Stirling1(n-k,4) * k * a(k).

a(n) = Sum_{k=1..floor(n/4)} (-1)^(k-1) * (4*k)! * Stirling1(n,4*k)/(k * 24^k). - Seiichi Manyama, Jan 23 2025

Mathematica

nmax = 23; CoefficientList[Series[Log[1 + Log[1 + x]^4/4!], {x, 0, nmax}], x] Range[0, nmax]! // Drop[#, 4] &
a[n_] := a[n] = StirlingS1[n, 4] - (1/n) Sum[Binomial[n, k] StirlingS1[n - k, 4] k a[k], {k, 1, n - 1}]; Table[a[n], {n, 4, 23}]

Crossrefs

Cf. A000454, A003713, A346944, A346945, A346947.

Cf. A346976.

Sequence in context: A038235 A354390 A354318 * A000454 A347003 A379674

Adjacent sequences: A346943 A346944 A346945 * A346947 A346948 A346949

Keyword

sign,changed

Author

Ilya Gutkovskiy, Aug 08 2021

Status

approved