A381880
Expansion of (1/x) * Series_Reversion( x * (1-x)^3 / C(x) ), where C(x) is the g.f. of A000108.
Original entry on oeis.org
1, 4, 27, 223, 2052, 20199, 208205, 2219149, 24261279, 270581313, 3066581130, 35216499786, 408919039968, 4792955710138, 56633333886618, 673881539636365, 8067939162382594, 97117925556632184, 1174721577627568371, 14270877151754826473, 174044527062280321368
Offset: 0
A381881
Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 * C(x)) ), where C(x) is the g.f. of A000108.
Original entry on oeis.org
1, 3, 14, 82, 547, 3958, 30249, 240362, 1966235, 16449495, 140093989, 1210575512, 10587490383, 93540456103, 833619150838, 7484887130882, 67645312129491, 614872423359187, 5617522739173495, 51556112664387720, 475105557839611760, 4394434006611790855
Offset: 0
A381860
G.f. A(x) satisfies A(x) = (1 + x)^3 * C(x*A(x)), where C(x) is the g.f. of A000108.
Original entry on oeis.org
1, 4, 12, 55, 327, 2157, 15141, 110853, 836790, 6465309, 50876776, 406335099, 3285202335, 26835060422, 221128733649, 1835973630276, 15344202894457, 128983332603009, 1089803313492966, 9250137181234430, 78837133437062307, 674408139329393187, 5788618956395607745
Offset: 0
-
a(n) = sum(k=0, n, binomial(3*k+1, k)*binomial(3*k+3, n-k)/(3*k+1));
A381907
Expansion of (1/x) * Series_Reversion( x / ((1+x)^3 * B(x)) ), where B(x) is the g.f. of A001764.
Original entry on oeis.org
1, 4, 25, 197, 1783, 17646, 185622, 2039617, 23149542, 269367631, 3196544816, 38539697456, 470773651286, 5813914938293, 72470441063067, 910587733474165, 11521140613913305, 146659482494039073, 1876975898990490298, 24137070792680577688, 311724732112458291945
Offset: 0
-
a(n) = sum(k=0, n, binomial(n+3*k+1, k)*binomial(3*n+3, n-k)/(n+3*k+1));
Showing 1-4 of 4 results.