A307363 Expansion of e.g.f. Sum_{j>=0} log(1 + x)^j / Product_{k=1..j} (1 - k*log(1 + x)).

1, 1, 3, 20, 218, 3514, 77386, 2220504, 80085792, 3533917704, 186779329704, 11623513158960, 839754709300800, 69603737430736560, 6552428441847854640, 694531396130434062720, 82265733994694038784640, 10816812417663289139328000, 1569560370536552329095091200

Offset

0,3

Links

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

Formula

a(n) = Sum_{k=0..n} Stirling1(n,k)*k!*Bell(k).

Mathematica

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

Crossrefs

Cf. A000110, A006252, A137341, A307362.

Sequence in context: A365438 A113333 A206405 * A052851 A262233 A058477

Adjacent sequences: A307360 A307361 A307362 * A307364 A307365 A307366

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 05 2019

Status

approved