A377889 -id:A377889 - cp's OEIS frontend

A377888 E.g.f. A(x) satisfies A(x) = exp(x * A(x))/(1 - x*A(x)^2).

1, 2, 17, 289, 7541, 267041, 11974645, 650666731, 41560476809, 3052145052433, 253400719220801, 23470964805942083, 2399562226994185885, 268404500411311273465, 32606551238103342068717, 4275233840499570086190331, 601753408713140793660643985, 90500525005651471292191270433

Offset: 0

Seiichi Manyama, Nov 10 2024

nonn

Cf. A352410, A377831, A377889.

Cf. A371318.

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

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

A380724 E.g.f. A(x) satisfies A(x) = exp(x * A(x)^3) / (1 - x*A(x)^3).

Original entry on oeis.org

1, 2, 29, 862, 39461, 2454296, 193406953, 18475039808, 2075062993865, 268013104242688, 39139481641977461, 6377306725457207552, 1147019426037344539501, 225728971809041691392000, 48248339461852786811399489, 11131014193619108036340637696, 2756799306857952163745291500433

Offset: 0

Seiichi Manyama, Jan 30 2025

nonn

Cf. A377831, A380723.
Cf. A373324, A377889.
Cf. A360609.

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

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

cp's OEIS Frontend

A377888 E.g.f. A(x) satisfies A(x) = exp(x * A(x))/(1 - x*A(x)^2).

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