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 A065755 Triangle of Gandhi polynomial coefficients. 2
 1, 1, 5, 10, 10, 5, 31, 230, 755, 1440, 1760, 1430, 770, 260, 45, 6721, 60655, 250665, 628535, 1067865, 1299570, 1166945, 783720, 393855, 146025, 38500, 6630, 585, 5850271, 59885980, 285597890, 843288660, 1727996845, 2610132070, 3012643620 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS First column is A065756. Second column is A065757. LINKS Table of n, a(n) for n=1..35. Michael Domaratzki, Combinatorial Interpretations of a Generalization of the Genocchi Numbers, Journal of Integer Sequences, Vol. 7 (2004), Article 04.3.6. FORMULA 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). EXAMPLE Irregular triangle begins: 1; 1, 5, 10, 10, 5; 31, 230, 755, 1440, 1760, 1430, 770, 260, 45; 6721, ... MATHEMATICA 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 *) CROSSREFS Cf. A065756, A065757, A065747, A065748, A036970. Sequence in context: A291380 A280718 A321357 * A346007 A135912 A200990 Adjacent sequences: A065752 A065753 A065754 * A065756 A065757 A065758 KEYWORD easy,nonn,tabf AUTHOR Mike Domaratzki (mdomaratzki(AT)alumni.uwaterloo.ca), Nov 17 2001 STATUS approved

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Last modified August 14 08:37 EDT 2024. Contains 375159 sequences. (Running on oeis4.)