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A375363
Expansion of 1/( (1 + x)^2 * (1 - x*(1 + x)^3) ).
1
1, -1, 5, 1, 19, 30, 102, 242, 666, 1718, 4555, 11937, 31435, 82615, 217301, 571372, 1502572, 3951188, 10390340, 27322972, 71850149, 188941251, 496850977, 1306548125, 3435774983, 9034913514, 23758733842, 62477347430, 164294064510, 432037221810
OFFSET
0,3
FORMULA
a(n) = -a(n-1) + 4*a(n-2) + 10*a(n-3) + 10*a(n-4) + 5*a(n-5) + a(n-6).
a(n) = Sum_{k=0..n} binomial(3*k-2,n-k).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(1/((1+x)^2*(1-x*(1+x)^3)))
(PARI) a(n) = sum(k=0, n, binomial(3*k-2, n-k));
CROSSREFS
Cf. A375362.
Sequence in context: A286232 A147437 A147369 * A066480 A136394 A145372
KEYWORD
sign
AUTHOR
Seiichi Manyama, Aug 13 2024
STATUS
approved