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A369297 Expansion of (1/x) * Series_Reversion( x * (1-x)^2 * (1-x^3) ). 4
1, 2, 7, 31, 153, 806, 4440, 25266, 147364, 876282, 5292527, 32378125, 200218715, 1249456536, 7858638756, 49766595855, 317051378103, 2030589300596, 13066646029059, 84439101344619, 547746622599561, 3565472378360110, 23282050305073680, 152466688160732190 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(n+k,k) * binomial(3*n-3*k+1,n-3*k).
a(n) = (1/(n+1)) * [x^n] 1/( (1-x)^2 * (1-x^3) )^(n+1). - Seiichi Manyama, Feb 14 2024
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)^2*(1-x^3))/x)
(PARI) a(n, s=3, t=1, u=2) = 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. A370273.
Sequence in context: A369622 A323632 A369265 * A256672 A366052 A368931
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 18 2024
STATUS
approved

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Last modified June 22 14:17 EDT 2024. Contains 373587 sequences. (Running on oeis4.)