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

Author

Mike Domaratzki (mdomaratzki(AT)alumni.uwaterloo.ca), Nov 17 2001

Keywords

• easy
• nonn
• tabf

Comments

First column is A065756. Second column is A065757.

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.

Crossrefs

Cf. A065756, A065757, A065747, A065748, A036970.

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).