A361090 -id:A361090 - cp's OEIS frontend

A361091 E.g.f. satisfies A(x) = exp( x/(1 - x/A(x)^2) ).

1, 1, 3, 1, -71, -19, 10051, 12349, -3185391, -9346247, 1797304771, 9717361721, -1582301193527, -13722004186331, 2000705907453891, 25552516703201461, -3432004488804778079, -60960914621687232271, 7660860906885122096515

Offset: 0

Seiichi Manyama, Mar 01 2023

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Winston de Greef, Table of n, a(n) for n = 0..380

Cf. A161630, A212722, A212917, A361090, A361092.

Cf. A361068, A361096.

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

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

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!.

A365035 E.g.f. satisfies A(x) = exp(x * (1 + x/A(x))).

Original entry on oeis.org

1, 1, 3, 1, -11, 61, 301, -6299, 7561, 903673, -9019079, -145636919, 4305630781, 7516191541, -2037845181371, 22442805921901, 944219385367441, -29922880660473359, -288352494154313999, 32071808922904896913, -273044292430852251899

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, A365036, A365037.

Cf. A361090.

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x+lambertw(x^2*exp(-x)))))

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

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

cp's OEIS Frontend

A361091 E.g.f. satisfies A(x) = exp( x/(1 - x/A(x)^2) ).

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

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A365035 E.g.f. satisfies A(x) = exp(x * (1 + x/A(x))).

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