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A369504
Expansion of (1/x) * Series_Reversion( x / ((1+x)^2+x^3)^2 ).
3
1, 4, 22, 142, 1005, 7546, 59033, 475962, 3927204, 33001024, 281449964, 2429922400, 21196031340, 186521336460, 1653830553417, 14761130834428, 132516050272100, 1195778542160992, 10839917478886459, 98671228898404032, 901509955793840923
OFFSET
0,2
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(2*n+2,k) * binomial(4*n-2*k+4,n-3*k).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2+x^3)^2)/x)
(PARI) a(n) = sum(k=0, n\3, binomial(2*n+2, k)*binomial(4*n-2*k+4, n-3*k))/(n+1);
CROSSREFS
Cf. A369212.
Sequence in context: A366677 A190271 A045744 * A243626 A369485 A104991
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 25 2024
STATUS
approved