A122031 a(n) = a(n - 1) + (n - 1)*a(n - 2).

1, 2, 3, 7, 16, 44, 124, 388, 1256, 4360, 15664, 59264, 231568, 942736, 3953120, 17151424, 76448224, 350871008, 1650490816, 7966168960, 39325494464, 198648873664, 1024484257408, 5394759478016, 28957897398400

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

Cf. A000898, A062267, A121966, A122021, A122022.

Sequence in context: A227546 A301902 A332885 * A246829 A296231 A089125

Adjacent sequences: A122028 A122029 A122030 * A122032 A122033 A122034

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