A386990 Decimal expansion of Sum_{k>=0} 2/(k!*(k! + 1)).

2, 3, 8, 4, 4, 2, 7, 3, 8, 7, 9, 7, 1, 4, 2, 8, 8, 2, 1, 1, 6, 4, 4, 8, 0, 4, 9, 2, 3, 8, 0, 4, 4, 8, 1, 8, 4, 6, 1, 4, 9, 8, 5, 7, 0, 6, 4, 6, 6, 9, 8, 7, 8, 4, 8, 4, 1, 7, 2, 0, 3, 9, 5, 2, 0, 8, 9, 0, 0, 3, 8, 3, 7, 7, 6, 3, 0, 4, 4, 7, 1, 1, 5, 3, 9, 1, 3, 2, 1, 6, 2, 4, 2, 6, 7, 8, 5, 5, 9, 3, 9, 6, 9, 5, 2, 3

Offset

1,1

Comments

Sum of reciprocals of A055555 (triangular numbers of factorials).

Links

Kelvin Voskuijl, Table of n, a(n) for n = 1..20000

Formula

Equals Sum_{k>=0} 1/A055555(k).

Example

2.3844273879714288211644804923804481846149857064...

Maple

evalf(sum(2/(n!*(n!+1)), n=0..infinity), 120);  # Alois P. Heinz, Aug 13 2025

Prog

(PARI) suminf(k=0, 2/(k!*(k!+1)))
(PARI) sumpos(k=0, 1/binomial(k!+1, 2)) \\ Charles R Greathouse IV, Aug 19 2025

Crossrefs

Cf. A000217, A070910 (of n!^2), A055555, A091131 (of n!).

Sequence in context: A349003 A079555 A100870 * A210688 A328428 A195794

Adjacent sequences: A386987 A386988 A386989 * A386991 A386992 A386993

Keyword

nonn,cons

Author

Kelvin Voskuijl, Aug 12 2025

Status

approved