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A369296 Expansion of (1/x) * Series_Reversion( x * (1-x) * (1-x^3)^2 ). 4
1, 1, 2, 7, 24, 84, 315, 1225, 4859, 19646, 80739, 336050, 1413587, 6000777, 25674462, 110598855, 479286932, 2088036939, 9139604421, 40174594432, 177267942918, 784889441217, 3486198469890, 15529021825140, 69355660644738, 310509670642611, 1393296782758244 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(2*n+k+1,k) * binomial(2*n-3*k,n-3*k).
a(n) = (1/(n+1)) * [x^n] 1/( (1-x) * (1-x^3)^2 )^(n+1). - Seiichi Manyama, Feb 14 2024
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)*(1-x^3)^2)/x)
(PARI) a(n, s=3, t=2, u=1) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((u+1)*(n+1)-s*k-2, n-s*k))/(n+1);
CROSSREFS
Cf. A370274.
Sequence in context: A000777 A369266 A144170 * A297345 A052986 A053368
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 18 2024
STATUS
approved

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Last modified July 13 04:46 EDT 2024. Contains 374267 sequences. (Running on oeis4.)