A378045 -id:A378045 - cp's OEIS frontend

A378043 E.g.f. satisfies A(x) = (1+x) * exp( x * (1+x) * A(x)^2 ).

1, 2, 13, 190, 4045, 116746, 4251289, 187255174, 9684799961, 575477786674, 38638577549701, 2893159369162030, 239045577899472997, 21604942464613062010, 2120362938300115706513, 224568728344893756230326, 25529660577970226603535793, 3100816199696659908092912866

Offset: 0

Seiichi Manyama, Nov 15 2024

nonn

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

Cf. A378019, A378044.
Cf. A377894, A378045.
Cf. A377894.

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

E.g.f.: (1+x) * exp( -LambertW(-2*x*(1+x)^3)/2 ).

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

A378046 E.g.f. satisfies A(x) = (1+x) * exp(x * A(x)^3 / (1+x)^2).

Original entry on oeis.org

1, 2, 11, 169, 4049, 132881, 5542495, 280694135, 16730578625, 1147444968385, 89015365063991, 7707022678811567, 736734708409976017, 77070404075178587633, 8757816984586841345231, 1074244834335107678837191, 141469329806979182825146625, 19908315372027482035799282177

Offset: 0

Seiichi Manyama, Nov 15 2024

nonn

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

Cf. A377826, A378045.

Cf. A363478.

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

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

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

cp's OEIS Frontend

A378043 E.g.f. satisfies A(x) = (1+x) * exp( x * (1+x) * A(x)^2 ).

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