A371832 a(n) = denominator(Sum_{k=1..n} k^2/k!).

1, 1, 1, 2, 6, 8, 40, 720, 1680, 13440, 362880, 1209600, 4435200, 68428800, 296524800, 29059430400, 1307674368000, 6974263296000, 118562476032000, 6402373705728000, 445586448384000, 1430277488640000, 51090942171709440000, 374666909259202560000, 8617338912961658880000

Offset: 0

Author

Stefano Spezia, Apr 07 2024

Keywords

• nonn
• frac

Links

• Eric Weisstein's World of Mathematics, Incomplete Gamma Function.
• Wikipedia, Incomplete gamma function.

Crossrefs

Cf. A019762, A030297, A371831.

Cf. A014973, A092043.

Programs

Mathematica

a[n_]:=Denominator[(2(E*Gamma[n+1,1]-1)-n)/n!]; Array[a,25,0]

PARI

a(n) = denominator(sum(k=1, n, k^2/k!)); \\ Michel Marcus, Apr 07 2024

Formula

a(n) = denominator((2*(e*Gamma(n+1, 1) - 1) - n)/n!).

a(n) = denominator(A030297(n)/n!).

Limit_{n->oo} A371831(n)/a(n) = 2*e = A019762.