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Triangle of Gandhi polynomial coefficients.
3

%I #13 May 11 2018 01:42:11

%S 1,1,4,6,4,15,88,220,304,250,120,28,1025,7308,23234,43420,52880,43880,

%T 25088,9680,2340,280,209135,1691024,6237520,13911400,20956610,

%U 22549360,17853780,10541440,4639740,1498280,341000,49920,3640,100482849

%N Triangle of Gandhi polynomial coefficients.

%C First column is A064625.

%H Michael Domaratzki, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL7/Domaratzki/doma23.html">Combinatorial Interpretations of a Generalization of the Genocchi Numbers</a>, Journal of Integer Sequences, Vol. 7 (2004), Article 04.3.6.

%H D. Dumont, <a href="http://dx.doi.org/10.1016/0012-365X(72)90039-8">Sur une conjecture de Gandhi concernant les nombres de Genocchi</a>, (in French), Discrete Mathematics 1 (1972) 321-327.

%H D. Dumont, <a href="http://dx.doi.org/10.1215/S0012-7094-74-04134-9">Interprétations combinatoires des nombres de Genocchi</a>, Duke Math. J., 41 (1974), 305-318.

%H D. Dumont, <a href="/A001469/a001469_3.pdf">Interprétations combinatoires des nombres de Genocchi</a>, Duke Math. J., 41 (1974), 305-318. (Annotated scanned copy)

%F 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).

%e Triangle starts

%e 1;

%e 1,4,6,4;

%e 15,88,220,304,250,120,28;

%e 1025,...

%Y Cf. A064625, A036970

%K easy,nonn,tabf

%O 1,3

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