A381773
Expansion of ( (1/x) * Series_Reversion( x/((1+x) * C(x))^3 ) )^(1/3), where C(x) is the g.f. of A000108.
Original entry on oeis.org
1, 2, 15, 157, 1913, 25427, 357546, 5229980, 78765793, 1213181593, 19021747383, 302595975502, 4871780511910, 79232327379407, 1299767617080662, 21481625997258747, 357350097625089497, 5978708468143961925, 100537111802285439375, 1698302173359384479307
Offset: 0
A381782
G.f. A(x) satisfies A(x) = (1 + x*A(x)^3) * C(x), where C(x) is the g.f. of A000108.
Original entry on oeis.org
1, 2, 9, 52, 342, 2437, 18331, 143320, 1153308, 9489487, 79470647, 675149665, 5804359859, 50402807459, 441433999816, 3894774605660, 34585663823538, 308867647484634, 2772256164853972, 24994569816424301, 226261997160303326, 2055711320495566962
Offset: 0
-
a(n) = sum(k=0, n, binomial(3*n-k+1, k)*binomial(3*n-3*k+1, n-k)/(3*n-k+1));
A381829
G.f. A(x) satisfies A(x) = C(x*A(x)) / (1 - x*A(x)^3), where C(x) is the g.f. of A000108.
Original entry on oeis.org
1, 2, 12, 97, 905, 9187, 98578, 1099980, 12636101, 148449436, 1775331503, 21541303494, 264533752068, 3281596216087, 41062196808517, 517655936768189, 6568539787903369, 83827401412072474, 1075254139150601581, 13855040994605807348, 179256835556387995412, 2327788724156294034612
Offset: 0
-
a(n) = sum(k=0, n, binomial(3*n+1, k)*binomial(4*n-3*k, n-k))/(3*n+1);
Showing 1-3 of 3 results.