A347022
Expansion of e.g.f. 1 / (1 - 5 * log(1 + x))^(1/5).
Original entry on oeis.org
1, 1, 5, 50, 720, 13650, 320370, 8967720, 291538080, 10795026840, 448484788680, 20658543923280, 1044915105622800, 57572197848878400, 3432143603792520000, 220109018869587398400, 15110184224165199667200, 1105545474191480800492800, 85881534014930659599571200
Offset: 0
-
nmax = 18; CoefficientList[Series[1/(1 - 5 Log[1 + x])^(1/5), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[StirlingS1[n, k] 5^k Pochhammer[1/5, k], {k, 0, n}], {n, 0, 18}]
A347021
Expansion of e.g.f. 1 / (1 - 4 * log(1 + x))^(1/4).
Original entry on oeis.org
1, 1, 4, 32, 364, 5444, 100520, 2210760, 56406240, 1637877600, 53327583360, 1924096475520, 76198487927040, 3285955396558080, 153273199794071040, 7689131281851770880, 412809183978447306240, 23616192920003184176640, 1434201753814306170808320
Offset: 0
-
nmax = 18; CoefficientList[Series[1/(1 - 4 Log[1 + x])^(1/4), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[StirlingS1[n, k] 4^k Pochhammer[1/4, k], {k, 0, n}], {n, 0, 18}]
A347023
E.g.f.: 1 / (1 - 6 * log(1 + x))^(1/6).
Original entry on oeis.org
1, 1, 6, 72, 1254, 28794, 819888, 27869316, 1101032100, 49570797780, 2505156062472, 140417898936336, 8644973807845368, 579908437058338920, 42098286646367326368, 3288252917244250703664, 274974019392668843164176, 24510436934573885695407504, 2319947117871178825560902112
Offset: 0
-
nmax = 18; CoefficientList[Series[1/(1 - 6 Log[1 + x])^(1/6), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[StirlingS1[n, k] 6^k Pochhammer[1/6, k], {k, 0, n}], {n, 0, 18}]
A365599
Expansion of e.g.f. 1 / (1 - 3 * log(1 + x))^(2/3).
Original entry on oeis.org
1, 2, 8, 54, 498, 5868, 83940, 1413480, 27375240, 599437440, 14641665120, 394657325280, 11635613604000, 372469741813440, 12864889063033920, 476870475257550720, 18882021780125953920, 795381867831610978560, 35515223076159203880960
Offset: 0
-
a[n_] := Sum[Product[3*j + 2, {j, 0, k - 1}] * StirlingS1[n, k], {k, 0, n}]; Array[a, 19, 0] (* Amiram Eldar, Sep 13 2023 *)
-
a(n) = sum(k=0, n, prod(j=0, k-1, 3*j+2)*stirling(n, k, 1));
Showing 1-4 of 4 results.
Comments