A185221 -id:A185221 - cp's OEIS frontend

A238274 Decimal expansion of abs(LambertW(-1)).

1, 3, 7, 4, 5, 5, 7, 0, 1, 0, 7, 4, 3, 7, 0, 7, 4, 8, 6, 5, 3, 0, 0, 9, 3, 0, 5, 6, 7, 6, 9, 6, 6, 2, 6, 7, 2, 3, 4, 4, 2, 9, 7, 6, 3, 6, 5, 3, 7, 6, 2, 6, 5, 0, 0, 1, 0, 9, 6, 5, 7, 1, 0, 6, 3, 2, 4, 2, 1, 6, 6, 9, 5, 6, 5, 6, 4, 8, 7, 1, 5, 1, 7, 1, 3, 8, 3, 6, 7, 0, 0, 6, 4, 1, 9, 6, 4, 9, 4, 0, 0, 6, 8, 2, 4

Offset: 1

Vaclav Kotesovec, Feb 24 2014

			1.37455701074370748653...

G. C. Greubel, Table of n, a(n) for n = 1..5000
Stanislav Sykora, Fixed points of the mappings exp(z) and -exp(z) in C, 2016.

Cf. A009306, A030178, A177380, A185221.

RealDigits[N[Abs[LambertW[-1]], 105]][[1]]

A367078 E.g.f. satisfies A(x) = 1 + log(1 + x*A(x)^2).

Original entry on oeis.org

1, 1, 3, 14, 82, 514, 2508, -12328, -820752, -22232232, -498433320, -9865850688, -159373484448, -1136343398880, 65056426313760, 4663237803223680, 210535052582008320, 7821007002377349120, 242387957802121971840, 5333182310844833642496

Offset: 0

Seiichi Manyama, Nov 07 2023

sign

Cf. A185221, A367079.

Cf. A367080, A367153.

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

a(n) = (2*n)! * Sum_{k=0..n} Stirling1(n,k)/(2*n-k+1)!.

A366729 E.g.f. satisfies A(x) = 1 + log(1 + x*A(x)^2)/A(x).

Original entry on oeis.org

1, 1, 1, -4, -36, 14, 3100, 22112, -374640, -9520320, 9674808, 4085208192, 55207595520, -1640647901088, -69445046214336, 103240707929088, 71686341699216384, 1439635203885275136, -60449514895261440000, -3608840044036879934976

Offset: 0

Seiichi Manyama, Nov 08 2023

sign

Cf. A185221, A367179.

Cf. A365438, A367180.

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

a(n) = Sum_{k=0..n} (2*n-k)!/(2*n-2*k+1)! * Stirling1(n,k).

A367079 E.g.f. satisfies A(x) = 1 + log(1 + x*A(x)^3).

Original entry on oeis.org

1, 1, 5, 47, 654, 12084, 278682, 7708056, 248678784, 9168447600, 380274659760, 17524760349216, 888364833282000, 49125202031205936, 2942774373267939168, 189829708902667840320, 13118899353628035596544, 966975804677206274688000

Offset: 0

Seiichi Manyama, Nov 07 2023

a(131) is negative. - Vaclav Kotesovec, Nov 07 2023

Vaclav Kotesovec, Table of n, a(n) for n = 0..358

Cf. A185221, A367078.

Cf. A367152, A367154.

Table[(3*n)! * Sum[StirlingS1[n,k]/(3*n-k+1)!, {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Nov 07 2023 *)

a(n) = (3*n)!*sum(k=0, n, stirling(n, k, 1)/(3*n-k+1)!);

a(n) = (3*n)! * Sum_{k=0..n} Stirling1(n,k)/(3*n-k+1)!.

A367179 E.g.f. satisfies A(x) = 1 + log(1 + x*A(x)^3)/A(x)^2.

Original entry on oeis.org

1, 1, 1, -7, -74, 14, 10736, 124032, -1695672, -81281688, -528840024, 47385631512, 1540148366736, -12438137705904, -2292918626509536, -48210827445848832, 2456594159904115200, 177787615056364279296, 782103240212585461632

Offset: 0

Seiichi Manyama, Nov 08 2023

sign

Cf. A185221, A366729.

a(n) = sum(k=0, n, (3*n-2*k)!/(3*n-3*k+1)!*stirling(n, k, 1));

a(n) = Sum_{k=0..n} (3*n-2*k)!/(3*n-3*k+1)! * Stirling1(n,k).

cp's OEIS Frontend

A238274 Decimal expansion of abs(LambertW(-1)).

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A367078 E.g.f. satisfies A(x) = 1 + log(1 + x*A(x)^2).

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A366729 E.g.f. satisfies A(x) = 1 + log(1 + x*A(x)^2)/A(x).

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A367079 E.g.f. satisfies A(x) = 1 + log(1 + x*A(x)^3).

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A367179 E.g.f. satisfies A(x) = 1 + log(1 + x*A(x)^3)/A(x)^2.

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