A065748 Triangle of Gandhi polynomial coefficients.

1, 1, 4, 6, 4, 15, 88, 220, 304, 250, 120, 28, 1025, 7308, 23234, 43420, 52880, 43880, 25088, 9680, 2340, 280, 209135, 1691024, 6237520, 13911400, 20956610, 22549360, 17853780, 10541440, 4639740, 1498280, 341000, 49920, 3640, 100482849

Offset: 1

Author

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

Keywords

• easy
• nonn
• tabf

Comments

First column is A064625.

Examples

			Triangle starts
1;
1,4,6,4;
15,88,220,304,250,120,28;
1025,...
		

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. A064625, A036970

Formula

Let B(X, n) = X^4 (B(X+1, n-1) - B(X, n-1)), B(X, 1) = X^4; then the (i, j)-th entry in the table is the coefficient of X^(5+j) in B(X, i).