A354751 Expansion of e.g.f. 1 / (1 - log(1 + 4*x) / 4).

1, 1, -2, 14, -152, 2264, -42832, 982512, -26484096, 820207488, -28692711168, 1118821622016, -48112717347840, 2261868010650624, -115400220781209600, 6350152838136428544, -374874781697133871104, 23632196147497381625856, -1584445791263626895228928

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = Sum_{k=0..n} Stirling1(n,k) * k! * 4^(n-k).

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * (k-1)! * (-4)^(k-1) * a(n-k).

Mathematica

nmax = 18; CoefficientList[Series[1/(1 - Log[1 + 4 x]/4), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[StirlingS1[n, k] k! 4^(n - k), {k, 0, n}], {n, 0, 18}]

Prog

(PARI) my(x='x + O('x^20)); Vec(serlaplace(1/(1-log(1+4*x)/4))) \\ Michel Marcus, Jun 06 2022

Crossrefs

Cf. A006252, A326324, A352071, A354147, A354237, A354264, A354750.

Sequence in context: A036079 A121227 A250916 * A211398 A219430 A301931

Adjacent sequences: A354748 A354749 A354750 * A354752 A354753 A354754

Keyword

sign

Author

Ilya Gutkovskiy, Jun 06 2022

Status

approved