A396161 First column of the triangular array with T(0, m) = m^m and T(n, m) = T(n - 1, m + 3) - T(n - 1, m + 2).

1, 23, 40662, 339512814, 7833320861072, 385274862872862320, 34651074659044387342080, 5148782075953899427664208008, 1175932058880268594539875051459264, 391109408932914016441213394462369295744, 181653878605153955962729835740045223980699520, 113939186843560221433330434261292079705499930804224

Offset

0,2

Comments

This sequence is obtained by iterating the shift-difference operator E^2*(E - 1) 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..n} (-1)^(n - k)*binomial(n, k)*(2*n + k)^(2*n + k), with 0^0 = 1.

Example

The triangular array begins:
  m:   0     1         2          3          4       5      ...
  -------------------------------------------------------------
  n =  0     1         1          4          27      256    ...
  n =  1     23        40662      339512814    ...
  n =  2     40662     339512814      ...
  n =  3     339512814     ...
a(1) = 3^3 - 2^2 = 23.

Crossrefs

Cf. A000312, A395765, A069856.

Sequence in context: A273192 A233210 A173369 * A185695 A101699 A122148

Adjacent sequences: A396158 A396159 A396160 * A396162 A396163 A396164

Keyword

nonn

Author

Dalton Heilig, May 18 2026

Status

approved