A107283 E.g.f. exp(x)*(x^2+x+2)/(1-x).

2, 5, 16, 59, 254, 1297, 7820, 54791, 438394, 3945629, 39456392, 434020435, 5208245366, 67707189929, 947900659204, 14218509888287, 227496158212850, 3867434689618741, 69613824413137664, 1322662663849615979, 26453253276992319982, 555518318816838720065

Offset: 0

Author

Creighton Dement, May 19 2005

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A030297.

Programs

Mathematica

CoefficientList[Series[E^x*(x^2+x+2)/(1-x), {x, 0, 20}], x]* Table[n!, {n, 0, 20}] (* Vaclav Kotesovec, Oct 17 2012 *)

PARI

x='x+O('x^66); Vec(serlaplace(exp(x)*(x^2+x+2)/(1-x))) \\ Joerg Arndt, May 15 2013

Formula

Recurrence: (4*n+3)*a(n) = (4*n^2 + 7*n + 20)*a(n-1) - (4*n^2 + 16*n - 11)*a(n-2) + 9*(n-2)*a(n-3). - Vaclav Kotesovec, Oct 17 2012

a(n) ~ 4*e*n!. - Vaclav Kotesovec, Oct 17 2012