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

0,6

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).

Links

Table of n, a(n) for n=0..54.

Example

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.

Sequence in context: A291820 A309124 A078341 * A199459 A316649 A065329

Adjacent sequences: A371759 A371760 A371761 * A371763 A371764 A371765

Keyword

nonn,tabl

Author

Peter Luschny, Apr 06 2024

Status

approved