A223515 Triangle T(n,k) represents the coefficients of (x^13*d/dx)^n, where n=1,2,3,...; generalization of Stirling numbers of second kind A008277, Lah-numbers A008297.

1, 13, 1, 325, 39, 1, 12025, 1807, 78, 1, 589225, 102375, 5785, 130, 1, 35942725, 6936475, 466830, 14105, 195, 1, 2623818925, 549241875, 41948725, 1538810, 29120, 273, 1, 223024608625, 49858620175, 4198780950, 177364005, 4130490, 53690, 364, 1

Offset

1,2

Links

Table of n, a(n) for n=1..36.

Example

Triangle begins:
             1;
            13,           1;
           325,          39,          1;
         12025,        1807,         78,         1;
        589225,      102375,       5785,       130,       1;
      35942725,     6936475,     466830,     14105,     195,     1
    2623818925,   549241875,   41948725,   1538810,   29120,   273,   1;
  223024608625, 49858620175, 4198780950, 177364005, 4130490, 53690, 364, 1;

Maple

b[0]:=f(x):
for j from 1 to 10 do
b[j]:=simplify(x^13*diff(b[j-1], x$1));
end do;
# Recurrence
a := proc(j, n, N) option remember;
   if j < 0 or j > n then 0 elif n = 0 then 1
   else a(j-1, n-1, N)+((N-1)*(n-1)+j)*a(j, n-1, N);
   end if; end proc:
for n from 0 to 8 do print(seq(a(j, n, 13), j=1..n)): end: # Brendan McKay, Mar 03 2026

Crossrefs

Cf. A008277, A019538, A035342, A035469, A049029, A049385, A092082, A132056, A223511-A223522, A223168-A223172, A223523-A223532.

Sequence in context: A278594 A120392 A133371 * A281092 A010223 A010222

Adjacent sequences: A223512 A223513 A223514 * A223516 A223517 A223518

Keyword

nonn,easy,tabl

Author

Udita Katugampola, Mar 23 2013

Status

approved