A052809 -id:A052809 - cp's OEIS frontend

A351739 Expansion of e.g.f. 1/(1 + log(1-x))^x.

1, 0, 2, 6, 40, 295, 2688, 28588, 348864, 4802922, 73652110, 1245046836, 23003289912, 461188427544, 9972307487660, 231341792369010, 5731422576446208, 151032969213699536, 4218265874407103640, 124471244064061267032, 3869361472890037713560

Offset: 0

Seiichi Manyama, May 20 2022

nonn

Cf. A052801, A052809, A354122, A354123.

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+log(1-x))^x))

a(0) = 1; a(n) = Sum_{k=1..n} A052809(k) * binomial(n-1,k-1) * a(n-k).

a(n) ~ n! * exp(n) / (Gamma(1 - 1/exp(1)) * n^(1/exp(1)) * (exp(1) - 1)^(n + 1 - 1/exp(1))). - Vaclav Kotesovec, Jun 04 2022

A354083 Expansion of e.g.f. (1 + log(1-x))^x.

Original entry on oeis.org

1, 0, -2, -6, -16, -55, -288, -2128, -19808, -219546, -2816530, -41002236, -666782136, -11961352104, -234327748900, -4972665181170, -113552835539328, -2774993356571920, -72238332282154344, -1995222148760626392, -58268719729725843880, -1793842001139571701696

Offset: 0

Seiichi Manyama, May 26 2022

sign

Cf. A052809, A351739, A354416.

my(N=30, x='x+O('x^N)); Vec(serlaplace((1+log(1-x))^x))

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=-sum(j=1, i, j*sum(k=1, j-1, (k-1)!*abs(stirling(j-1, k, 1)))*binomial(i-1, j-1)*v[i-j+1])); v;

a(0) = 1; a(n) = -Sum_{k=1..n} A052809(k) * binomial(n-1,k-1) * a(n-k).

cp's OEIS Frontend

A351739 Expansion of e.g.f. 1/(1 + log(1-x))^x.

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A354083 Expansion of e.g.f. (1 + log(1-x))^x.

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Author

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PARI

PARI

Formula