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A025760
7th-order Vatalan numbers (generalization of Catalan numbers).
8
1, 1, 22, 680, 24074, 917414, 36618492, 1508943612, 63643109727, 2732349490669, 118957846271104, 5237911268468572, 232794783971436296, 10427673857731312064, 470213556090357498728, 21325335129901497816528
OFFSET
0,3
LINKS
FORMULA
G.f.: 7/(6 + (1 - 49*x)^(1/7)).
a(n) = (-1)^(n+1) * 7^(2*n+1) * Sum_{k>=0} (-1/6)^(k+1) * binomial(k/7,n). - Seiichi Manyama, Aug 04 2024
MATHEMATICA
Table[SeriesCoefficient[7/(6 + (1 - 49*x)^(1/7)), {x, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Dec 29 2012 *)
KEYWORD
nonn
STATUS
approved