A097967 a(n) = Sum_{k=1..n} (P(n,k) + C(n,k)).

0, 2, 7, 22, 79, 356, 2019, 13826, 109855, 986920, 9865123, 108507158, 1302065439, 16926805676, 236975181187, 3554627504842, 56874039618751, 966858672535760, 17403456103546563, 330665665962928286, 6613313319249128575

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = Sum_{k=1..n} n!(k!+1) / k!(n-k)! = Sum_{k=1..n} P(n, k)+2^n-1 = A007526(n) - A000225(n) - 1 = A097656(n) - 2.

Conjecture: a(n) +(-n-6)*a(n-1) +(6*n+7)*a(n-2) +(-13*n+14)*a(n-3) +4*(3*n-8)*a(n-4) +4*(-n+4)*a(n-5)=0. - R. J. Mathar, May 29 2013

Example

a(2) = 7 because P(2,1) = 2, P(2,2) = 2 while C(2,1)= 2, C(2,2) = 1 and 2 + 2 + 2 + 1 = 7.

Maple

A097967 := proc(n)
    add(n!*(k!+1)/k!/(n-k)!, k=1..n) ;
end proc: # R. J. Mathar, May 29 2013

Mathematica

f[n_] := Sum[n!(k! + 1)/(k!(n - k)!), {k, n}]; Table[ f[n], {n, 0, 20}] (* Robert G. Wilson v, Sep 24 2004 *)

Crossrefs

Cf. A097656, A007526, A000225.

Sequence in context: A132838 A047095 A110137 * A360861 A052879 A007867

Adjacent sequences: A097964 A097965 A097966 * A097968 A097969 A097970

Keyword

nonn

Author

Ross La Haye, Sep 21 2004

Extensions

Edited by Robert G. Wilson v, Sep 24 2004

Status

approved