A377895 -id:A377895 - cp's OEIS frontend

A377894 E.g.f. satisfies A(x) = (1 + x) * exp(x * A(x)^2).

1, 2, 11, 142, 2725, 71026, 2339719, 93311758, 4371948137, 235418287042, 14327098759171, 972533690209390, 72854996624174989, 5970582808814848498, 531359818098465084863, 51034785131352404960686, 5261620527219949295345233, 579593410301187097865649922

Offset: 0

Seiichi Manyama, Nov 11 2024

nonn

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

Cf. A377826, A377895.

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

E.g.f.: (1+x) * exp( -LambertW(-2*x*(1+x)^2)/2 ).
E.g.f.: ( -LambertW(-2*x*(1+x)^2)/(2*x) )^(1/2).
a(n) = n! * Sum_{k=0..n} (2*k+1)^(k-1) * binomial(2*k+1,n-k)/k!.

A378044 E.g.f. satisfies A(x) = (1+x) * exp( x * (1+x) * A(x)^3 ).

Original entry on oeis.org

1, 2, 17, 349, 10661, 444161, 23447635, 1500738989, 112954047113, 9777254959729, 956963374613471, 104510139881448797, 12599380858829314093, 1662018439019972570681, 238128379446158082330779, 36825779588890274967294061, 6113887910300601007096973585, 1084611999181162104894547358561

Offset: 0

Seiichi Manyama, Nov 15 2024

nonn

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

Cf. A378019, A378043.

Cf. A377895.

a(n) = n!*sum(k=0, n, (3*k+1)^(k-1)*binomial(4*k+1, n-k)/k!);

E.g.f.: (1+x) * exp( -LambertW(-3*x*(1+x)^4)/3 ).

a(n) = n! * Sum_{k=0..n} (3*k+1)^(k-1) * binomial(4*k+1,n-k)/k!.

cp's OEIS Frontend

A377894 E.g.f. satisfies A(x) = (1 + x) * exp(x * A(x)^2).

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