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Triangle of Gandhi polynomial coefficients.
2

%I #12 Jul 08 2017 11:58:21

%S 1,1,5,10,10,5,31,230,755,1440,1760,1430,770,260,45,6721,60655,250665,

%T 628535,1067865,1299570,1166945,783720,393855,146025,38500,6630,585,

%U 5850271,59885980,285597890,843288660,1727996845,2610132070,3012643620

%N Triangle of Gandhi polynomial coefficients.

%C First column is A065756. Second column is A065757.

%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.

%F 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).

%e Irregular triangle begins:

%e 1;

%e 1, 5, 10, 10, 5;

%e 31, 230, 755, 1440, 1760, 1430, 770, 260, 45;

%e 6721, ...

%t 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 *)

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

%K easy,nonn,tabf

%O 1,3

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

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Last modified September 20 20:48 EDT 2024. Contains 376078 sequences. (Running on oeis4.)