A161632 -id:A161632 - cp's OEIS frontend

A377579 E.g.f. satisfies A(x) = (1 + x * exp(x*A(x)))^4.

1, 4, 20, 204, 3112, 61220, 1523064, 45456292, 1586426720, 63461164932, 2862300600040, 143766016251044, 7959047336014416, 481550056915454020, 31615435540393172888, 2238661916541220434660, 170070509857455107126464, 13798559748847266924993284, 1190848786811966457102586824

Offset: 0

Seiichi Manyama, Nov 02 2024

nonn

Cf. A161632, A377578.

Cf. A377580, A377581.

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

E.g.f.: B(x)^4, 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+4,k)/( (n-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

A377579 E.g.f. satisfies A(x) = (1 + x * exp(x*A(x)))^4.

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