A377744 -id:A377744 - cp's OEIS frontend

A377742 E.g.f. satisfies A(x) = exp(x) / (1 - x * A(x))^2.

1, 3, 23, 331, 7133, 205901, 7470475, 326932299, 16768124217, 986753701657, 65548017270791, 4852285640543639, 396133183892522389, 35359325061987638661, 3426053898460864501251, 358128187005971803014211, 40172982580368589391407217, 4813677071886578522596221233

Offset: 0

Seiichi Manyama, Nov 05 2024

nonn

Cf. A194471, A377743, A377744.
Cf. A001339, A377745.
Cf. A377503.

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

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

A377743 E.g.f. satisfies A(x) = exp(x) / (1 - x * A(x))^3.

Original entry on oeis.org

1, 4, 43, 853, 25141, 989581, 48885187, 2910389875, 202958554057, 16233163690537, 1465257396236551, 147359765665925143, 16341437664329027389, 1981169884084699982701, 260701144663332062732491, 37007345616327485166160651, 5637148375602304430334748945, 917186940500490837457393476817

Offset: 0

Seiichi Manyama, Nov 06 2024

nonn

Cf. A194471, A377742, A377744.

Cf. A373324, A377504.

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

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

cp's OEIS Frontend

A377742 E.g.f. satisfies A(x) = exp(x) / (1 - x * A(x))^2.

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