OFFSET
0,2
FORMULA
a(n) = [x^n] 1/(((1-x)^2-x^3) * (1-x)^(2*n)).
a(n) = binomial(1+3*n, n)*hypergeom([1, (1-n)/3, (2-n)/3, -n/3], [-1-3*n, 1+n, 3/2+n], 27/4). - Stefano Spezia, Apr 06 2024
From Vaclav Kotesovec, Apr 08 2024: (Start)
Recurrence: 2*n*(2*n - 1)*(671*n^4 - 4757*n^3 + 11743*n^2 - 11533*n + 3516)*a(n) = (44957*n^6 - 350256*n^5 + 997889*n^4 - 1236792*n^3 + 563834*n^2 + 39768*n - 60480)*a(n-1) - 10*(19459*n^6 - 156741*n^5 + 461272*n^4 - 575421*n^3 + 211099*n^2 + 106572*n - 60480)*a(n-2) + (93269*n^6 - 753150*n^5 + 2221631*n^4 - 2772678*n^3 + 999800*n^2 + 543408*n - 302400)*a(n-3) - 3*(3*n - 8)*(3*n - 7)*(671*n^4 - 2073*n^3 + 1498*n^2 + 366*n - 360)*a(n-4).
a(n) ~ 3^(3*n + 5/2) / (11 * sqrt(Pi*n) * 2^(2*n)). (End)
PROG
(PARI) a(n) = sum(k=0, n\3, binomial(3*n-k+1, n-3*k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 05 2024
STATUS
approved