A082428 a(1) = 1; a(n) = 3 + n * Sum_{k=1..n-1} a(k).

1, 5, 21, 111, 693, 4989, 40743, 372507, 3771633, 41907033, 507075099, 6638074023, 93486209157, 1409484384213, 22652427603423, 386601431098419, 6982988349215193, 133087542655630737, 2669144605482372003, 56192518010155200063, 1239045022123922161389, 28557037652760872672013

Offset: 1

Author

Benoit Cloitre, Apr 24 2003

Keywords

• nonn

Crossrefs

Cf. A007808, A074143, A082425, A082427, A082430, A383436, A383437.

Cf. A001339.

Formula

for n>=2 a(n) = ceiling(n*(3e-7)*n!).

From Seiichi Manyama, Apr 27 2025: (Start)

E.g.f.: -3 - x + (-7*x + 3*exp(x))/(1-x)^2.

a(n) = -7 * n * n! + 3 * Sum_{k=0..n} (k+1)! * binomial(n,k) for n > 1.

a(n) = (n^2 * a(n-1) - 3)/(n-1) for n > 2.

a(n) = (n+2) * a(n-1) - (n-1) * a(n-2) for n > 3. (End)