A065755 Triangle of Gandhi polynomial coefficients.
1, 1, 5, 10, 10, 5, 31, 230, 755, 1440, 1760, 1430, 770, 260, 45, 6721, 60655, 250665, 628535, 1067865, 1299570, 1166945, 783720, 393855, 146025, 38500, 6630, 585, 5850271, 59885980, 285597890, 843288660, 1727996845, 2610132070, 3012643620
Offset: 1
Examples
Irregular triangle begins: 1; 1, 5, 10, 10, 5; 31, 230, 755, 1440, 1760, 1430, 770, 260, 45; 6721, ...
Links
- Michael Domaratzki, Combinatorial Interpretations of a Generalization of the Genocchi Numbers, Journal of Integer Sequences, Vol. 7 (2004), Article 04.3.6.
Programs
-
Mathematica
B[X_, 1] := X^5; B[X_, n_] := B[X, n] = X^5 (B[X+1, n-1] - B[X, n-1]) // Expand; row[1] = {1}; row[n_] := List @@ B[X, n] /. X -> 1; Array[row, 5] // Flatten (* Jean-François Alcover, Jul 08 2017 *)
Formula
Let B(X, n) = X^5 (B(X+1, n-1) - B(X, n-1)), B(X, 1) = X^5; then the (i, j)-th entry in the table is the coefficient of X^(4+j) in B(X, i).
Comments