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

1,2

Comments

Sequence is related to asymptotic of A229001.

Links

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

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)).

Example

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

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 *)

Crossrefs

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

Sequence in context: A219843 A064855 A088504 * A369243 A189425 A266169

Adjacent sequences: A229088 A229089 A229090 * A229092 A229093 A229094

Keyword

nonn

Author

Vaclav Kotesovec, Sep 13 2013

Status

approved