A352271 -id:A352271 - cp's OEIS frontend

A352270 Expansion of e.g.f. 1/(2 - exp(x) + log(1 - x)).

1, 2, 10, 75, 751, 9405, 141361, 2478959, 49683047, 1120216645, 28064294201, 773391141325, 23250533411821, 757231705088131, 26558855360366239, 998051946325525971, 40006049065833007891, 1703833370634756077097, 76833773059665726636621

Offset: 0

Seiichi Manyama, Mar 10 2022

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..390

Cf. A000670, A352139, A352146, A352271.

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(x)+log(1-x))))

a(n) = if(n==0, 1, sum(k=1, n, ((k-1)!+1)*binomial(n, k)*a(n-k)));

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

A352293 Expansion of e.g.f. 1/(2 - exp(x) - x/(1 + x)).

Original entry on oeis.org

1, 2, 7, 43, 335, 3301, 38925, 535851, 8429139, 149173321, 2933274593, 63446532271, 1497102036567, 38269877372637, 1053531222709269, 31074273060116083, 977649690943993979, 32680936703516606737, 1156722832021068313833, 43216064601701505904983

Offset: 0

Seiichi Manyama, Mar 11 2022

nonn

Vaclav Kotesovec, Table of n, a(n) for n = 0..400

Cf. A006155, A352271, A352292.

m = 19; Range[0, m]! * CoefficientList[Series[1/(2 - Exp[x] - x/(1 + x)), {x, 0, m}], x] (* Amiram Eldar, Mar 11 2022 *)

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(x)-x/(1+x))))

a(n) = if(n==0, 1, sum(k=1, n, ((-1)^(k-1)*k!+1)*binomial(n, k)*a(n-k)));

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

a(n) ~ n! * (1+r)^2 / ((3 + r*(3+r)) * r^(n+1)), where r = 0.50855472406037552... is the root of the equation 2 - exp(r) - r/(1+r) = 0. - Vaclav Kotesovec, Jul 25 2022

cp's OEIS Frontend

A352270 Expansion of e.g.f. 1/(2 - exp(x) + log(1 - x)).

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

PARI

Formula

A352293 Expansion of e.g.f. 1/(2 - exp(x) - x/(1 + x)).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

PARI

Formula