A352070
Expansion of e.g.f. 1/(1 - log(1 + 3*x))^(1/3).
Original entry on oeis.org
1, 1, 1, 10, 10, 604, -1844, 107344, -1201400, 42193576, -875584376, 29853569008, -880141783184, 32865860907424, -1216481572723616, 51296026356128512, -2244334822166729600, 106984479644794783360, -5358207684820194270080, 286466413246622566048000
Offset: 0
-
m = 19; Range[0, m]! * CoefficientList[Series[(1 - Log[1 + 3*x])^(-1/3), {x, 0, m}], x] (* Amiram Eldar, Mar 05 2022 *)
Table[Sum[3^(n-k) * Product[3*j+1, {j,0,k-1}] * StirlingS1[n,k], {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Sep 07 2023 *)
-
a[n]:=if n=0 then 1 else n!*sum(a[n-k]*(2/n/3-1/k)*(-3)^k/(n-k)!,k,1,n);
makelist(a[n],n,0,50); /* Tani Akinari, Sep 07 2023 */
-
my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-log(1+3*x))^(1/3)))
-
a(n) = sum(k=0, n, 3^(n-k)*prod(j=0, k-1, 3*j+1)*stirling(n, k, 1));
A352075
Expansion of e.g.f. sqrt(1 - log(1 - 2*x)).
Original entry on oeis.org
1, 1, 1, 5, 25, 209, 1961, 23589, 321105, 5100801, 90384369, 1792247973, 39011436201, 928869511569, 23953711043289, 666047439187077, 19847286284835105, 631267636613496705, 21339849019758468705, 764149215124570567365, 28891697037933017586105
Offset: 0
-
m = 20; Range[0, m]! * CoefficientList[Series[(1 - Log[1 - 2*x])^(1/2), {x, 0, m}], x] (* Amiram Eldar, Mar 05 2022 *)
-
my(N=20, x='x+O('x^N)); Vec(serlaplace(sqrt(1-log(1-2*x))))
-
a(n) = sum(k=0, n, (-2)^(n-k)*prod(j=0, k-1, -2*j+1)*stirling(n, k, 1));
A352114
Expansion of e.g.f. (1 - log(1 - 4*x))^(1/4).
Original entry on oeis.org
1, 1, 1, 17, 129, 2529, 42753, 1080561, 28269825, 910318785, 31733067777, 1260881785041, 54451914027393, 2588888715388065, 132887134408562433, 7371812870053439409, 437841346658159352321, 27782111830252836998529, 1873198439610729939408897
Offset: 0
-
m = 18; Range[0, m]! * CoefficientList[Series[(1 - Log[1 - 4*x])^(1/4), {x, 0, m}], x] (* Amiram Eldar, Mar 05 2022 *)
-
my(N=20, x='x+O('x^N)); Vec(serlaplace((1-log(1-4*x))^(1/4)))
-
a(n) = sum(k=0, n, (-4)^(n-k)*prod(j=0, k-1, -4*j+1)*stirling(n, k, 1));
A352122
Expansion of e.g.f. (2 - exp(-3*x))^(1/3).
Original entry on oeis.org
1, 1, -5, 37, -413, 6421, -128285, 3125557, -89781053, 2969440021, -111109062365, 4639580153077, -213856576973693, 10784605095793621, -590598038062108445, 34901993971832092597, -2213771863243583654333, 150004882482828402563221
Offset: 0
-
m = 17; Range[0, m]! * CoefficientList[Series[(2 - Exp[-3*x])^(1/3), {x, 0, m}], x] (* Amiram Eldar, Mar 05 2022 *)
-
my(N=20, x='x+O('x^N)); Vec(serlaplace((2-exp(-3*x))^(1/3)))
-
a(n) = sum(k=0, n, (-3)^(n-k)*prod(j=0, k-1, -3*j+1)*stirling(n, k, 2));
Showing 1-4 of 4 results.