A361091 -id:A361091 - cp's OEIS frontend

A361090 E.g.f. satisfies A(x) = exp( x/(1 - x/A(x)) ).

1, 1, 3, 7, -11, -239, -179, 24991, 192025, -3955391, -89483399, 552615031, 46231717621, 254468241457, -26683006147979, -571848064714289, 14926049610344881, 825004339886219521, -2973711136010539535, -1134313888244827421465, -17734152216328857754739

Offset: 0

Seiichi Manyama, Mar 01 2023

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Winston de Greef, Table of n, a(n) for n = 0..399

Cf. A161630, A212722, A212917, A361091, A361092.

Cf. A361067, A361095.

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

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

A361092 E.g.f. satisfies A(x) = exp( x/(1 - x/A(x)^3) ).

Original entry on oeis.org

1, 1, 3, -5, -107, 1041, 20701, -440033, -8464455, 343190593, 5639857561, -423764450889, -4968055259771, 754544622295153, 3846355902999429, -1818148417882379729, 6637679490204153841, 5658469355898945338625, -84578525845602646639823

Offset: 0

Seiichi Manyama, Mar 01 2023

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Winston de Greef, Table of n, a(n) for n = 0..368

Cf. A161630, A212722, A212917, A361090, A361091.

Cf. A361069, A361097.

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

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

A365036 E.g.f. satisfies A(x) = exp(x * (1 + x/A(x)^2)).

Original entry on oeis.org

1, 1, 3, -5, -23, 521, -1829, -71021, 1319697, 5905297, -683965709, 8664974891, 311864420473, -13981842414695, 6694007756619, 16448800124183491, -448649039951220959, -13236887251789967071, 1210629233913421852387, -12065049302884271631269

Offset: 0

Seiichi Manyama, Aug 17 2023

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Eric Weisstein's World of Mathematics, Lambert W-Function.

Cf. A125500, A143768, A363354, A363529, A365035, A365037.

Cf. A361091.

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

E.g.f.: exp( x + LambertW(2*x^2*exp(-2*x))/2 ).

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

cp's OEIS Frontend

A361090 E.g.f. satisfies A(x) = exp( x/(1 - x/A(x)) ).

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A361092 E.g.f. satisfies A(x) = exp( x/(1 - x/A(x)^3) ).

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A365036 E.g.f. satisfies A(x) = exp(x * (1 + x/A(x)^2)).

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