A330352
Expansion of e.g.f. -Sum_{k>=1} log(1 - log(1 + x)^k) / k.
Original entry on oeis.org
1, 1, 0, 10, -68, 818, -9782, 130730, -1835752, 27408672, -438578616, 7697802264, -150743052528, 3293454634416, -78787556904864, 2014008113598432, -54001416897306240, 1504891127666322048, -43527807706621236480, 1311515508480252542208
Offset: 1
-
nmax = 20; CoefficientList[Series[-Sum[Log[1 - Log[1 + x]^k]/k, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest
Table[Sum[StirlingS1[n, k] (k - 1)! DivisorSigma[0, k], {k, 1, n}], {n, 1, 20}]
A330494
a(n) = Sum_{k=1..n} (-1)^(n-k) * Stirling1(n,k) * (k-1)! * sigma(k), where sigma = A000203.
Original entry on oeis.org
1, 4, 19, 129, 1018, 9912, 111074, 1416398, 20295208, 323437728, 5657339928, 107765338920, 2223272444976, 49399021063584, 1175549092374672, 29822113966614768, 803485297880792064, 22917198585269729664, 689927737384840662144, 21861972842959846530432
Offset: 1
-
Table[Sum[(-1)^(n-k) * StirlingS1[n, k] * (k-1)! * DivisorSigma[1, k], {k, 1, n}], {n, 1, 20}]
nmax = 20; Rest[CoefficientList[Series[Sum[Log[1/(1 - x)]^k/(k (1 - Log[1/(1 - x)]^k)), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!]
-
a(n) = sum(k=1, n, (-1)^(n-k)*stirling(n, k, 1)*(k-1)!*sigma(k)); \\ Michel Marcus, Dec 16 2019
A330495
a(n) = Sum_{k=1..n} (-1)^(n-k) * Stirling1(n,k) * (k-1)! * sigma_2(k), where sigma_2 = A001157.
Original entry on oeis.org
1, 6, 37, 307, 2858, 32060, 405830, 5777354, 91400200, 1593023040, 30251766840, 622016655816, 13777150847952, 327040289212320, 8280040187137200, 222696435041359824, 6341359225470493440, 190609840724078576256, 6031297367477133540480, 200389374367707186619776
Offset: 1
-
Table[Sum[(-1)^(n-k) * StirlingS1[n, k] * (k-1)! * DivisorSigma[2, k], {k, 1, n}], {n, 1, 20}]
nmax = 20; Rest[CoefficientList[Series[Sum[Log[1/(1 - x)]^k/(k*(1 - Log[1/(1 - x)]^k)^2), {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]!]
-
a(n) = sum(k=1, n, (-1)^(n-k)*stirling(n, k, 1)*(k-1)!*sigma(k, 2)); \\ Michel Marcus, Dec 16 2019
A330498
Expansion of e.g.f. Sum_{k>=1} log(1 + log(1/(1 - x))^k) / k.
Original entry on oeis.org
0, 1, 1, 6, 24, 152, 1230, 12646, 141274, 1730984, 23920800, 379364664, 6766026168, 131337466608, 2713274041296, 59397879195456, 1386647548658496, 34745321580075648, 934708252265232768, 26835517455387452928, 815158892950448937984
Offset: 0
-
nmax = 20; CoefficientList[Series[Sum[Log[1+Log[1/(1-x)]^k]/k, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]!
Showing 1-4 of 4 results.
