A380491 -id:A380491 - cp's OEIS frontend

A380492 a(n) = n! * Sum_{k=0..n} binomial(2*n-2,k)/(n-k)!.

1, 1, 7, 73, 1045, 19081, 424051, 11109337, 335262313, 11453449105, 436944953791, 18412283563081, 849345673881277, 42570185481576793, 2303643608370636715, 133859418832759525081, 8312945340897388101841, 549460711493172343519777, 38513032385247860120975863

Offset: 0

Seiichi Manyama, Jan 25 2025

nonn

Cf. A082545, A152059, A251568, A293985, A343832, A380491, A380493.

PARI
```
a(n) = n!*pollaguerre(n, n-2, -1);
```

a(n) = n! * LaguerreL(n, n-2, -1).

a(n) = n! * [x^n] exp(x/(1 - x))/(1 - x)^(n-1).

A380493 a(n) = n! * Sum_{k=0..n} binomial(2*n+3,k)/(n-k)!.

Original entry on oeis.org

1, 6, 57, 748, 12585, 259026, 6315001, 178134552, 5711078673, 205209960670, 8171229107481, 357235056697476, 17014791129640057, 877089297426429738, 48657292133825026905, 2890717184573264397616, 183125115830192864360481, 12323226433255671469949622

Offset: 0

Seiichi Manyama, Jan 25 2025

nonn

Cf. A082545, A152059, A251568, A293985, A343832, A380491, A380492.

PARI
```
a(n) = n!*pollaguerre(n, n+3, -1);
```

a(n) = n! * LaguerreL(n, n+3, -1).

a(n) = n! * [x^n] exp(x/(1 - x))/(1 - x)^(n+4).

cp's OEIS Frontend

A380492 a(n) = n! * Sum_{k=0..n} binomial(2*n-2,k)/(n-k)!.

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