A377579 -id:A377579 - cp's OEIS frontend

A377580 E.g.f. satisfies A(x) = (1 + x * exp(x*A(x)^2))^2.

1, 2, 6, 66, 920, 17450, 425772, 12443438, 428469456, 16947065682, 757343738900, 37752522755222, 2076633137032632, 124956870908294906, 8165077881669520476, 575775223046122068510, 43582446983541508540832, 3524622951250814296207010, 303306411871327203664657956

Offset: 0

Seiichi Manyama, Nov 02 2024

nonn

Cf. A377579, A377581.

a(n) = n!*sum(k=0, n, k^(n-k)*binomial(4*n-4*k+2, k)/((2*n-2*k+1)*(n-k)!));

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A377581.

a(n) = n! * Sum_{k=0..n} k^(n-k) * binomial(4*n-4*k+2,k)/( (2*n-2*k+1)*(n-k)! ).

A377581 E.g.f. satisfies A(x) = 1 + x * exp(x*A(x)^4).

Original entry on oeis.org

1, 1, 2, 27, 340, 6485, 156486, 4532647, 155359016, 6116223465, 272369488330, 13537882005131, 742838308204092, 44605728508797469, 2909444391161677838, 204844046364505460655, 15484082153045052133456, 1250714994867101307618257, 107511883999692161772696210

Offset: 0

Seiichi Manyama, Nov 02 2024

nonn

Cf. A161631, A364978, A364979.

Cf. A377579, A377580.

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

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

A377578 E.g.f. satisfies A(x) = (1 + x * exp(x*A(x)))^3.

Original entry on oeis.org

1, 3, 12, 105, 1308, 21375, 441018, 10896123, 315264792, 10449447579, 390569672910, 16257117737223, 745842771924660, 37396841181068343, 2034701509480503906, 119398947940954110915, 7517149983020119420848, 505442237612562154098099, 36150074712773275030075926

Offset: 0

Seiichi Manyama, Nov 02 2024

nonn

Cf. A161632, A377579.

Cf. A364979.

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

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A364979.

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

cp's OEIS Frontend

A377580 E.g.f. satisfies A(x) = (1 + x * exp(x*A(x)^2))^2.

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A377581 E.g.f. satisfies A(x) = 1 + x * exp(x*A(x)^4).

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A377578 E.g.f. satisfies A(x) = (1 + x * exp(x*A(x)))^3.

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