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
A381783
G.f. A(x) satisfies A(x) = (1 + x*A(x)^3) * C(x*A(x)), where C(x) is the g.f. of A000108.
Original entry on oeis.org
1, 2, 11, 79, 645, 5682, 52643, 505575, 4987933, 50250625, 514787110, 5346336739, 56161123273, 595667090038, 6370314162095, 68616488830785, 743733580011957, 8106009997644507, 88783190884441892, 976705067814061730, 10787334777299825522, 119569153425125828365
Offset: 0
-
a(n) = sum(k=0, n, binomial(3*n+1, k)*binomial(3*n-2*k+1, n-k))/(3*n+1);
A381827
G.f. A(x) satisfies A(x) = C(x) / (1 - x*A(x)^3), where C(x) is the g.f. of A000108.
Original entry on oeis.org
1, 2, 10, 69, 562, 5042, 48100, 478547, 4908338, 51522174, 550758208, 5974753990, 65608248500, 727835313461, 8144965594184, 91834891588099, 1042244963201914, 11896871741939462, 136493661712053752, 1573151972820654218, 18205626549920314728, 211468167403628323318
Offset: 0
-
a(n) = sum(k=0, n, binomial(3*n-k+1, k)*binomial(4*n-4*k, n-k)/(3*n-k+1));
Showing 1-3 of 3 results.