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

0,4

Links

Table of n, a(n) for n=0..24.

Eric Weisstein's World of Mathematics, Incomplete Gamma Function.

Wikipedia, Incomplete gamma function.

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A019762, A030297, A371831.

Cf. A014973, A092043.

Sequence in context: A095239 A192009 A065953 * A118211 A050552 A105607

Adjacent sequences: A371829 A371830 A371831 * A371833 A371834 A371835

Keyword

nonn,frac

Author

Stefano Spezia, Apr 07 2024

Status

approved