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A371405
Expansion of (1/x) * Series_Reversion( x / ( (1+x) * (1+3*x)^3 ) ).
0
1, 10, 136, 2134, 36379, 654670, 12239560, 235407070, 4627854244, 92576970280, 1878395043232, 38564373070090, 799651963174978, 16722655896174004, 352289843771100400, 7469327989417602862, 159263992188702829900, 3412969567344634872952
OFFSET
0,2
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..n} 3^k * binomial(3*(n+1),k) * binomial(n+1,n-k).
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x/((1+x)*(1+3*x)^3))/x)
(PARI) a(n) = sum(k=0, n, 3^k*binomial(3*(n+1), k)*binomial(n+1, n-k))/(n+1);
CROSSREFS
Cf. A364923.
Sequence in context: A129803 A065024 A026244 * A261503 A096619 A376064
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 21 2024
STATUS
approved