A026025 a(n) = (n!)^2 * (1 + Sum_{k=0..n-1} 1/((k+1)(k!)^2)).

1, 2, 10, 93, 1492, 37305, 1342986, 65806321, 4211604552, 341139968721, 34113996872110, 4127793621525321, 594402281499646236, 100453985573440213897, 19688981172394281923826, 4430020763788713432860865, 1134085315529910638812381456, 327750656188144174616778240801, 106191212604958712575836150019542

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = n^2*a(n-1)+n. - Vladeta Jovovic, Apr 13 2003

For n>0, a(n) = floor((n!)^2 * (1 + I(1,2))), where I(n,x) is the modified Bessel function of the first kind. The error term erased by the floor is less than 1/n. - Mikhail Lavrov, Mar 02 2025

Prog

(PARI) a(n) = (n!)^2 * (1 + sum(k=0, n-1, 1/((k+1)*(k!)^2))); \\ Michel Marcus, Mar 02 2025

Crossrefs

Sequence in context: A260339 A205320 A254243 * A231375 A383219 A100622

Adjacent sequences: A026022 A026023 A026024 * A026026 A026027 A026028

Keyword

easy,nonn

Author

Brian Wallace (wallacebrianedward(AT)yahoo.co.uk), May 18 2001

Extensions

Corrected and extended by Matthew Conroy, May 22 2001

More terms from Michel Marcus, Mar 02 2025

Status

approved