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A377204
Expansion of 1/(1 - 4*x^2/(1-x))^(3/2).
2
1, 0, 6, 6, 36, 66, 236, 546, 1626, 4106, 11388, 29646, 79838, 209718, 557328, 1465970, 3869448, 10166370, 26726080, 70092570, 183756378, 481048010, 1258494768, 3289100958, 8590288128, 22418099982, 58467588768, 152388145382, 396954437202, 1033452111702, 2689186662552
OFFSET
0,3
FORMULA
a(n) = (2*(n-1)*a(n-1) + (3*n+6)*a(n-2) - 2*(2*n-3)*a(n-3))/n for n > 2.
a(n) = Sum_{k=0..floor(n/2)} (2*k+1) * binomial(2*k,k) * binomial(n-k-1,n-2*k).
PROG
(PARI) a(n) = sum(k=0, n\2, (2*k+1)*binomial(2*k, k)*binomial(n-k-1, n-2*k));
CROSSREFS
Cf. A377186.
Sequence in context: A056452 A183622 A176861 * A245131 A038260 A242087
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 20 2024
STATUS
approved