A371762 Triangle read by rows: the polynomial coefficients of the numerator of the rational solution of the linear recurrence equations of the rows of A371761.

1, 0, 1, 0, 1, 2, 0, 1, 7, 6, 0, 1, 19, 46, 24, 0, 1, 46, 251, 326, 120, 0, 1, 104, 1163, 3016, 2556, 720, 0, 1, 225, 4831, 23283, 35848, 22212, 5040, 0, 1, 473, 18523, 158531, 417148, 437228, 212976, 40320, 0, 1, 976, 66886, 976636, 4285549, 7084804, 5586444, 2239344, 362880

Offset: 0

Author

Peter Luschny, Apr 06 2024

Keywords

• nonn
• tabl

Comments

Let R(n) = N(n)/D(n) denote the ordinary rational generating function of row n of A371761 as given by its linear recurrence equation. N(n) is the row polynomial Sum_{k=0..n} T(n, k)*x^k and D(n) = Sum_{k=0..n} Stirling1(n+1, n+1-k)*x^k. Thus A371761(n, k) = [x^k] N(n)/D(n).

Examples

			Triangle starts:
  [0] 1;
  [1] 0, 1;
  [2] 0, 1,   2;
  [3] 0, 1,   7,     6;
  [4] 0, 1,  19,    46,     24;
  [5] 0, 1,  46,   251,    326,     120;
  [6] 0, 1, 104,  1163,   3016,    2556,     720;
  [7] 0, 1, 225,  4831,  23283,   35848,   22212,    5040;
  [8] 0, 1, 473, 18523, 158531,  417148,  437228,  212976,   40320;
  [9] 0, 1, 976, 66886, 976636, 4285549, 7084804, 5586444, 2239344, 362880;
.
The rational generating function for row 3 of A371761 is:
gf = (6*x^3 + 7*x^2 + x)/(-6*x^3 + 11*x^2 - 6*x + 1).
		

Crossrefs

Cf. A029767 (row sums), A000142 (main diagonal), A067318 (subdiagonal).

Cf. A371761.