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A377198
Expansion of 1/(1 - 4*x/(1-x)^2)^(3/2).
1
1, 6, 42, 278, 1794, 11382, 71338, 443046, 2732034, 16751462, 102235050, 621535158, 3766261506, 22758222294, 137186860842, 825211984710, 4954574749698, 29697908825286, 177746214414634, 1062416305340502, 6342559258130178, 37823152988963126, 225328426205608362
OFFSET
0,2
FORMULA
a(0) = 1; a(n) = 2 * Sum_{k=0..n-1} (3-k/n) * (n-k) * a(k).
a(n) = ((7*n-1)*a(n-1) - (7*n-20)*a(n-2) + (n-3)*a(n-3))/n for n > 2.
a(n) = Sum_{k=0..n} (2*k+1) * binomial(2*k,k) * binomial(n+k-1,n-k).
PROG
(PARI) a(n) = sum(k=0, n, (2*k+1)*binomial(2*k, k)*binomial(n+k-1, n-k));
CROSSREFS
Cf. A377194.
Sequence in context: A331706 A074429 A062310 * A229247 A105482 A242158
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 19 2024
STATUS
approved