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

1,3

Comments

First column is A064624.

Links

Table of n, a(n) for n=1..36.

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)

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).

Example

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

Crossrefs

Cf. A036970, A064624, A065748

Sequence in context: A333924 A173321 A191498 * A363398 A232309 A273043

Adjacent sequences: A065744 A065745 A065746 * A065748 A065749 A065750

Keyword

easy,nonn,tabf

Author

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

Status

approved