A065747 Triangle of Gandhi polynomial coefficients.

1, 1, 3, 3, 7, 30, 51, 42, 15, 145, 753, 1656, 1995, 1410, 567, 105, 6631, 39048, 100704, 149394, 140475, 86562, 34566, 8316, 945, 566641, 3656439, 10546413, 17972598, 20133921, 15581349, 8493555, 3246642, 841239, 135135, 10395

Offset: 1

Author

Mike Domaratzki (mdomaratzki(AT)alumni.uwaterloo.ca), Nov 16 2001

Keywords

• easy
• nonn
• tabf

Comments

First column is A064624.

Examples

			Triangle starts
1;
1, 3, 3;
7, 30, 51, 42, 15;
145, 753, 1656, 1995, 1410, 567, 105;
6631 ...
		

Links

• Michael Domaratzki, Combinatorial Interpretations of a Generalization of the Genocchi Numbers, Journal of Integer Sequences, Vol. 7 (2004), Article 04.3.6.
• D. Dumont, Sur une conjecture de Gandhi concernant les nombres de Genocchi, (in French), Discrete Mathematics 1 (1972) 321-327.
• D. Dumont, Interprétations combinatoires des nombres de Genocchi, Duke Math. J., 41 (1974), 305-318.
• D. Dumont, Interprétations combinatoires des nombres de Genocchi, Duke Math. J., 41 (1974), 305-318. (Annotated scanned copy)

Crossrefs

Cf. A036970, A064624, A065748

Formula

Let B(X, n) = X^3 (B(X+1, n-1) - B(X, n-1)), B(X, 1) = X^3; then the (i, j)-th entry is the table is the coefficient of X^(2+j) in B(X, i).