A371831 a(n) = numerator(Sum_{k=1..n} k^2/k!).

0, 1, 3, 9, 31, 43, 217, 3913, 9133, 73067, 1972819, 6576067, 24112247, 372017527, 1612075951, 157983443203, 7109254944151, 37916026368811, 644572448269793, 34806912206568841, 2422459091299663, 7775794614048301, 277759159408419360043, 2036900502328408640323, 46848711553553398727437

Offset

0,3

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

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

Limit_{n->oo} a(n)/A371832(n) = 2*e = A019762.

Mathematica

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

Prog

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

Crossrefs

Cf. A019762, A030297, A371832.

Cf. A014973, A092043.

Sequence in context: A292300 A058148 A031031 * A306526 A034550 A018370

Adjacent sequences: A371828 A371829 A371830 * A371832 A371833 A371834

Keyword

nonn,frac

Author

Stefano Spezia, Apr 07 2024

Status

approved