A396162 First column of the triangular array with T(0, m) = m^m and T(n, m) = T(n - 1, m + 3) - 2*T(n - 1, m + 2) + T(n - 1, m + 1).

1, 20, 35588, 298222584, 6893041104320, 339390744700600960, 30545941969311603920448, 4541087129383087067300766208, 1037530290355966843503848621711360, 345178211314328731754914550691807848448, 160358051712882281911114847531779916283438080, 100600852780499610741720532655118892927017005940736

Offset

0,2

Comments

This sequence is obtained by iterating the shift-difference operator E*(E - 1)^2 on f(m) = m^m and evaluating at m = 0, where E is the shift operator.

Links

Table of n, a(n) for n=0..11.

Formula

a(n) = Sum_{k=0..2*n} (-1)^k*binomial(2*n, k)*(n + k)^(n + k), with 0^0 = 1.

Example

The triangular array begins:
  m:        0         1          2          3         4     ...
  --------------------------------------------------------------
  n = 0     1         1          4          27        256   ...
  n = 1     20        35588      298222584    ...
  n = 2     35588     298222584      ...
  n = 3     298222584      ...

Crossrefs

Cf. A000312, A395764, A069856.

Sequence in context: A369948 A064487 A099187 * A129041 A129040 A159370

Adjacent sequences: A396159 A396160 A396161 * A396163 A396164 A396165

Keyword

nonn

Author

Dalton Heilig, May 18 2026

Status

approved