A352293 -id:A352293 - cp's OEIS frontend

A352292 Expansion of e.g.f. 1/(2 - exp(x) - x/(1 - x)).

1, 2, 11, 91, 1007, 13941, 231645, 4490739, 99496787, 2480012329, 68684121713, 2092433179431, 69540117508119, 2503694594140845, 97076021030158565, 4032791843669289883, 178701570260701316219, 8413561430997560725713, 419425619946011214516345

Offset: 0

Seiichi Manyama, Mar 11 2022

nonn

Cf. A002866, A352270, A352293.

m = 18; 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, (k!+1)*binomial(n, k)*a(n-k)));

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

A352295 Expansion of e.g.f. 1/(exp(x) - x/(1 + x)).

Original entry on oeis.org

1, 0, -3, 5, 29, -181, -401, 9645, -14183, -689257, 4826171, 55700633, -1024570955, -2770525005, 221566919911, -1028838834811, -49439771820367, 723165789334703, 9903852025111027, -362150510124039471, -463774017017434739, 169793689786411161995

Offset: 0

Seiichi Manyama, Mar 11 2022

sign

Cf. A352138, A352293, A352294.

m = 21; Range[0, m]! * CoefficientList[Series[1/(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/(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).

cp's OEIS Frontend

A352292 Expansion of e.g.f. 1/(2 - exp(x) - x/(1 - x)).

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A352295 Expansion of e.g.f. 1/(exp(x) - x/(1 + x)).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

PARI

PARI

Formula