A107055 Integer part of Sum_{k>=0} Sum_{j=0..k} n^j*A107045(k,j)/A107046(k,j).

1, 2, 4, 8, 14, 23, 37, 60, 94, 147, 227, 349, 533, 810, 1225, 1847, 2776, 4162, 6224, 9288, 13836, 20575, 30552, 45305, 67100, 99267, 146703, 216602, 319525, 470974, 693685, 1020998, 1501775, 2207604, 3243324, 4762421, 6989521, 10253264

Offset: 1

Author

Paul D. Hanna, May 17 2005

Keywords

• nonn

Comments

Limit a(n+1)/a(n) exists and is conjectured to equal exp(exp(-1)).

Crossrefs

Cf. A107045/A107046, A107047/A107048 (n=2), A107049/A107050 (n=3), A107051/A107052 (n=4), A107053/A107054 (n=5).

Programs

PARI

{a(n)=floor(sum(k=0,n+10,sum(j=0,k, n^j*(matrix(k+1,k+1,r,c,if(r>=c,1.*(r-1)^(c-1)))^-1)[k+1,j+1])))}

Formula

n^p = Sum_{k=0..n} p^k*Sum_{j=0..k} n^j*A107045(k, j)/A107046(k, j) for all nonnegative integers n and p.