A243227 -id:A243227 - cp's OEIS frontend

A226775 Decimal expansion of the number x other than -2 defined by x*exp(x) = -2/e^2.

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

Offset: 0

José María Grau Ribas, Jun 17 2013

			-0.4063757399599599076769581241248397582109975751811406350004954883....

G. C. Greubel, Table of n, a(n) for n = 0..10000
Index entries for transcendental numbers.

Cf. A106533, A187655, A187657, A217899, A217900, A226750, A243227, A245109, A247238, A258467, A337458.

RealDigits[N[ProductLog[-2/E^2], 105]][[1]] (* corrected by Vaclav Kotesovec, Feb 21 2014 *)

solve(x=-1, x=0, x*exp(x) + 2*exp(-2)) \\ G. C. Greubel, Nov 15 2017

Equals -2*A106533.

Equals LambertW(-2*exp(-2)).

A247238 a(n) = Stirling2(2*n+1, n).

Original entry on oeis.org

1, 15, 301, 7770, 246730, 9321312, 408741333, 20415995028, 1144614626805, 71187132291275, 4864251308951100, 362262620784874680, 29206898819153109600, 2534474684137526739000, 235535731151727520125765, 23339590705557273894321960

Offset: 1

Vladimir Kruchinin, Nov 28 2014

nonn

			O.g.f.: A(x) = x + 15*x^2 + 301*x^3 + 7770*x^4 + 246730*x^5 + 9321312*x^6 + ... where A(x) = 1^3*x*exp(-1^2*x) + 2^5*exp(-2^2*x)*x^2/2! + 3^7*exp(-3^2*x)*x^3/3! + 4^9*exp(-4^2*x)*x^4/4! + 5^11*exp(-5^2*x)*x^5/5! + ...

G. C. Greubel, Table of n, a(n) for n = 1..340

Cf. A048993, A007820, A217899, A243227, A226775.

Table[StirlingS2[2*n+1, n], {n, 1, 20}] (* Vaclav Kotesovec, Nov 29 2014 *)

vector(50, n, stirling(2*n+1, n, 2)) \\ Colin Barker, Nov 28 2014

a(n) = A243227(n) / (n-1)!. - Vaclav Kotesovec, Nov 29 2014
a(n) ~ 2^(2*n+1/2) * n^(n+1/2) / (sqrt(Pi) * sqrt(1-c) * exp(n) * c^n * (2-c)^(n+1)), where c = -LambertW(-2*exp(-2)) = 0.4063757399599599... (see A226775). - Vaclav Kotesovec, Nov 29 2014
O.g.f. Sum_{n>=1} n^(2*n+1) * x^n * exp(-n^2*x) / n! = Sum_{n>=1} a(n)*x^n. - Paul D. Hanna, Oct 09 2023

cp's OEIS Frontend

A226775 Decimal expansion of the number x other than -2 defined by x*exp(x) = -2/e^2.

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