A346845
E.g.f.: log(1 + x) / (1 - x)^3.
Original entry on oeis.org
1, 5, 29, 186, 1374, 11352, 105048, 1070640, 11978640, 145558080, 1914027840, 27035890560, 408891369600, 6585851059200, 112656894336000, 2038285492992000, 38915729475840000, 781515776369664000, 16475855040820224000, 363685261902133248000, 8391522945839007744000
Offset: 1
-
nmax = 21; CoefficientList[Series[Log[1 + x]/(1 - x)^3, {x, 0, nmax}], x] Range[0, nmax]! // Rest
Table[n! Sum[(-1)^(k + 1) Binomial[n - k + 2, 2]/k , {k, 1, n}], {n, 1, 21}]
Table[n!*(((-1)^n*(2*n + 5) - 4*n - 5)/8 + (n+1)*(n+2)*(Log[2] - (-1)^n * LerchPhi[-1, 1, 1 + n])/2), {n, 1, 21}] // Simplify (* Vaclav Kotesovec, Aug 06 2021 *)
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my(x='x+O('x^25)); Vec(serlaplace(log(1+x)/(1-x)^3)) \\ Michel Marcus, Aug 06 2021
A346846
E.g.f.: log(1 + x) / (1 - x)^4.
Original entry on oeis.org
1, 7, 50, 386, 3304, 31176, 323280, 3656880, 44890560, 594463680, 8453128320, 128473430400, 2079045964800, 35692494566400, 648044312832000, 12406994498304000, 249834635947008000, 5278539223415808000, 116768100285720576000, 2699047267616544768000, 65071515565786447872000
Offset: 1
-
nmax = 21; CoefficientList[Series[Log[1 + x]/(1 - x)^4, {x, 0, nmax}], x] Range[0, nmax]! // Rest
Table[n! Sum[(-1)^(k + 1) Binomial[n - k + 3, 3]/k , {k, 1, n}], {n, 1, 21}]
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my(x='x+O('x^25)); Vec(serlaplace(log(1+x)/(1-x)^4)) \\ Michel Marcus, Aug 06 2021
A346847
E.g.f.: log(1 + x) / (1 - x)^5.
Original entry on oeis.org
1, 9, 77, 694, 6774, 71820, 826020, 10265040, 137275920, 1967222880, 30092580000, 489584390400, 8443643040000, 153903497126400, 2956596769728000, 59712542813952000, 1264947863784192000, 28047600771531264000, 649672514944814592000, 15692497566512836608000, 394613964462556016640000
Offset: 1
-
nmax = 21; CoefficientList[Series[Log[1 + x]/(1 - x)^5, {x, 0, nmax}], x] Range[0, nmax]! // Rest
Table[n! Sum[(-1)^(k + 1) Binomial[n - k + 4, 4]/k , {k, 1, n}], {n, 1, 21}]
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my(x='x+O('x^25)); Vec(serlaplace(log(1+x)/(1-x)^5)) \\ Michel Marcus, Aug 06 2021
A302582
a(n) = n! * [x^n] log(1 + x)/(1 - x)^n.
Original entry on oeis.org
0, 1, 3, 29, 386, 6774, 146484, 3762744, 111868560, 3777096240, 142734788640, 5967788097600, 273488036169600, 13631083378617600, 734083968523046400, 42477063883483622400, 2628184745184816384000, 173147202267665649408000, 12100888735302910523904000, 894183767796064712795136000
Offset: 0
-
Table[n! SeriesCoefficient[Log[1 + x]/(1 - x)^n, {x, 0, n}], {n, 0, 19}]
Table[n! Sum[(-1)^(k + 1) Binomial[2 n - k - 1, n - k]/k, {k, 1, n}], {n, 0, 19}]
Join[{0}, Table[n^2 (2 (n - 1))! HypergeometricPFQ[{1, 1, 1 - n}, {2, 2 - 2 n}, -1]/n!, {n, 19}]]
Showing 1-4 of 4 results.