A304727 a(0) = 0, a(1) = 1, a(n) = n! * a(n-1) + a(n-2).

0, 1, 2, 13, 314, 37693, 27139274, 136781978653, 5515049406428234, 2001301128741459532573, 7262321535982523401207330634, 289888636287509191402441516910783773, 138857120603534969958797266489215885728367434

Offset

0,3

Comments

Also numerator of fraction equal to the continued fraction [ 0; 1!, 2!, ... , n! ].

Links

Seiichi Manyama, Table of n, a(n) for n = 0..43

Formula

a(n) ~ c * BarnesG(n+2), where c = 1.09066686013842761466853962605824103850541289039727399315605573072024... - Vaclav Kotesovec, Jun 05 2018

Example

a(1) =   1 because [ 0; 1! ]             = 1/1.
a(2) =   2 because [ 0; 1!, 2! ]         = 2/3.
a(3) =  13 because [ 0; 1!, 2!, 3! ]     = 13/19.
a(4) = 314 because [ 0; 1!, 2!, 3!, 4! ] = 314/459.

Crossrefs

Cf. A176232.

Sequence in context: A013106 A134485 A236551 * A355730 A075620 A336188

Adjacent sequences: A304724 A304725 A304726 * A304728 A304729 A304730

Keyword

nonn

Author

Seiichi Manyama, Jun 05 2018

Status

approved