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

1,3

Comments

First column is A065756. Second column is A065757.

Links

Table of n, a(n) for n=1..35.

Michael Domaratzki, Combinatorial Interpretations of a Generalization of the Genocchi Numbers, Journal of Integer Sequences, Vol. 7 (2004), Article 04.3.6.

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).

Example

Irregular triangle begins:
1;
1,      5,  10,   10,    5;
31,   230, 755, 1440, 1760, 1430, 770, 260, 45;
6721, ...

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 *)

Crossrefs

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

Sequence in context: A291380 A280718 A321357 * A346007 A135912 A200990

Adjacent sequences: A065752 A065753 A065754 * A065756 A065757 A065758

Keyword

easy,nonn,tabf

Author

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

Status

approved