OFFSET
0,2
COMMENTS
Equals the eigensequence of an infinite lower triangular matrix with (1, 1, 1, ...) in the main diagaonal, (1, 1, 2, 3, 4, 5, ...) in the subdiagonal and the rest zeros. - Gary W. Adamson, Apr 13 2009
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..795
FORMULA
E.g.f.: (1/2)*exp(x + x^2/2)*(2 - sqrt(2*exp(1)*Pi)*erf(1/sqrt(2)) + sqrt(2*exp(1)*Pi)*erf((1+x)/sqrt(2))). - Paul Abbott (paul(AT) physics.uwa.edu.au)
a(n) ~ (1/sqrt(2) + sqrt(Pi)/2*exp(1/2) * (1 - erf(1/sqrt(2)))) * n^(n/2)*exp(sqrt(n) - n/2 - 1/4) * (1+7/(24*sqrt(n))). - Vaclav Kotesovec, Dec 27 2012
MATHEMATICA
a[0] = 1; a[1] = 2; a[n_] := a[n] = a[n - 1] + (n - 1)*a[n - 2] Table[a[n], {n, 0, 30}]
Table[n!*SeriesCoefficient[1/2*Exp[x+x^2/2]*(2-Sqrt[2*E*Pi]*Erf[1/Sqrt[2]]+Sqrt[2*E*Pi]*Erf[(1+x)/Sqrt[2]]), {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec after Paul Abbott, Dec 27 2012 *)
RecurrenceTable[{a[0]==1, a[1]==2, a[n]==a[n-1]+(n-1)a[n-2]}, a, {n, 30}] (* Harvey P. Dale, Feb 21 2015 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Sep 13 2006
EXTENSIONS
Edited by N. J. A. Sloane, Sep 17 2006
Offset corrected by Vaclav Kotesovec, Dec 27 2012
STATUS
approved