A174639 A triangular sequence:f(n)=Sum[StirlingS2[n, k], {k, 1, n}];t(n,m)=Binomial[n, m]*f(m + 1)*f(n - m + 1)-Binomial[n,0]*f(1)*f(n+1)+1

1, 1, 1, 1, 4, 1, 1, 16, 16, 1, 1, 69, 99, 69, 1, 1, 318, 548, 548, 318, 1, 1, 1560, 3024, 3624, 3024, 1560, 1, 1, 8139, 17176, 23161, 23161, 17176, 8139, 1, 1, 45094, 101634, 149374, 168134, 149374, 101634, 45094, 1, 1, 264672, 629226, 989046, 1214082

Offset

0,5

Comments

Row sums are:

1, 2, 6, 34, 239, 1734, 12794, 96954, 760340, 6194054, 52490379,...

Links

Table of n, a(n) for n=0..49.

Formula

f(n)=Sum[StirlingS2[n, k], {k, 1, n}];

t(n,m)=Binomial[n, m]*f(m + 1)*f(n - m + 1)-Binomial[n,0]*f(1)*f(n+1)+1

Example

{1},
{1, 1},
{1, 4, 1},
{1, 16, 16, 1},
{1, 69, 99, 69, 1},
{1, 318, 548, 548, 318, 1},
{1, 1560, 3024, 3624, 3024, 1560, 1},
{1, 8139, 17176, 23161, 23161, 17176, 8139, 1},
{1, 45094, 101634, 149374, 168134, 149374, 101634, 45094, 1},
{1, 264672, 629226, 989046, 1214082, 1214082, 989046, 629226, 264672, 1},
{1, 1640931, 4079506, 6773431, 8898271, 9706099, 8898271, 6773431, 4079506, 1640931, 1}

Mathematica

f[n_] := Sum[StirlingS2[n, k], {k, 1, n}];
t[n_, m_] = Binomial[n, m]*f[m + 1]*f[n - m + 1]
Table[Table[t[n, m] - t[n, 0] + 1, {m, 0, n}], {n, 0, 10}];
Flatten[%]

Crossrefs

Sequence in context: A203846 A118185 A176483 * A173814 A176467 A034802

Adjacent sequences: A174636 A174637 A174638 * A174640 A174641 A174642

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Mar 25 2010

Status

approved