A229091 a(n) = ((-1)^n*(2^n-1) + Sum_{k>=1} (k^n*(k^2+k-1)/(k+2)!))/exp(1).

0, 2, 0, 14, 20, 152, 532, 2914, 14604, 83342, 494164, 3127016, 20810088, 145645866, 1067655656, 8177942670, 65292914084, 542226906224, 4674687594572, 41766307038106, 386112935883604, 3687989974641678, 36347655981682676, 369185211517110928, 3860146249155022160

Offset: 1

Author

Vaclav Kotesovec, Sep 13 2013

Keywords

• nonn

Comments

Sequence is related to asymptotic of A229001.

Examples

			Sequence A228997 (column k=7 of A229001) is asymptotic to n!*(532*exp(1)+127)*n, therefore a(7) = 532.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A229001, A228959, A229003, A228994, A228995, A228996, A228997, A228998, A228999, A229000.

Programs

Mathematica

Table[Simplify[((-1)^n*(2^n-1) + Sum[k^n*(k^2+k-1)/(k+2)!,{k,1,Infinity}])/E],{n,1,20}] (* from definition *)
Table[BellB[n] - BellB[n+1] + Sum[(-1)^j*(2^j*((2*n-j+1)/(j+1))-1) * BellB[n-j]*Binomial[n,j],{j,0,n}],{n,1,20}] (* faster *)

Formula

a(n) = Bell(n) - Bell(n+1) + Sum_{j=0..n} ((-1)^j*(2^j*((2*n-j+1)/(j+1))-1) * Bell(n-j) * C(n,j)).