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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
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).
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
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Apr 06 2024
STATUS
approved