A368283 -id:A368283 - cp's OEIS frontend

A368284 Expansion of e.g.f. exp(-2*x) / (1 + log(1 - x)).

1, -1, 3, 0, 32, 182, 1882, 20500, 260136, 3701968, 58565360, 1019110848, 19346296752, 397867297136, 8811800026928, 209100451072672, 5292665533921024, 142338738348972672, 4053176346277660288, 121828547313861426176, 3854597854165079424768

Offset: 0

Seiichi Manyama, Dec 19 2023

sign

Cf. A007840, A291979, A330149, A368283.

a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=(-2)^i+sum(j=1, i, (j-1)!*binomial(i, j)*v[i-j+1])); v;

a(n) = (-2)^n + Sum_{k=1..n} (k-1)! * binomial(n,k) * a(n-k).

A368444 Expansion of e.g.f. exp(x) / (1 + log(1 - 2*x)).

Original entry on oeis.org

1, 3, 17, 155, 1937, 30499, 577793, 12784155, 323427041, 9207390211, 291277318065, 10136705490779, 384848820035057, 15829002092015267, 701141988610115617, 33275461169171553371, 1684504951149122303169, 90604594879948059236099

Offset: 0

Seiichi Manyama, Dec 24 2023

nonn

Cf. A291979, A368445.

Cf. A343707, A368283.

a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+sum(j=1, i, 2^j*(j-1)!*binomial(i, j)*v[i-j+1])); v;

a(n) = 1 + Sum_{k=1..n} 2^k * (k-1)! * binomial(n,k) * a(n-k).

a(n) ~ sqrt(Pi) * exp(1/2 - exp(-1)/2) * 2^(n + 1/2) * n^(n + 1/2) / (exp(1) - 1)^(n+1). - Vaclav Kotesovec, Dec 25 2023

cp's OEIS Frontend

A368284 Expansion of e.g.f. exp(-2*x) / (1 + log(1 - x)).

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