A379934 -id:A379934 - cp's OEIS frontend

A379933 Expansion of e.g.f. 1/( exp(-x) - x )^2.

1, 4, 22, 158, 1408, 15002, 186100, 2634998, 41937136, 741170834, 14402727484, 305225470046, 7005711916840, 173134991854970, 4583675648417044, 129424786945875398, 3882446011526729440, 123304773913531035170, 4133369745467043807340, 145840627118145774415214

Offset: 0

Seiichi Manyama, Jan 06 2025

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..410

Cf. A072597, A379942, A379943.
Cf. A379934, A379936.
Cf. A358738, A377529.

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

a(n) = n!*sum(k=0, n, (k+1)*(k+2)^(n-k)/(n-k)!);

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A072597.

a(n) = n! * Sum_{k=0..n} (k+1) * (k+2)^(n-k)/(n-k)!.

A379936 E.g.f. A(x) satisfies A(x) = 1/( exp(-x*A(x)^(1/2)) - x )^2.

Original entry on oeis.org

1, 4, 30, 344, 5400, 108492, 2667952, 77811120, 2629399680, 101122817300, 4363964377344, 208925612290056, 10992411683169280, 630611992509716700, 39182624685283891200, 2621745777377998537568, 187969244952968687812608, 14377545994804829244970020

Offset: 0

Seiichi Manyama, Jan 06 2025

nonn

Cf. A379933, A379934.

Cf. A088690.

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

a(n) = 2*n!*sum(k=0, n, (n+2)^(k-1)*binomial(n+2, n-k)/k!);

E.g.f.: ( (1/x) * Series_Reversion( x*exp(-x)/(1+x) ) )^2.
E.g.f.: B(x)^2, where B(x) is the e.g.f. of A088690.
a(n) = 2 * n! * Sum_{k=0..n} (n+2)^(k-1) * binomial(n+2,n-k)/k!.

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A379933 Expansion of e.g.f. 1/( exp(-x) - x )^2.

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A379936 E.g.f. A(x) satisfies A(x) = 1/( exp(-x*A(x)^(1/2)) - x )^2.

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