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
A381787
G.f. A(x) satisfies A(x) = (1 + x) * C(x*A(x)), where C(x) is the g.f. of A000108.
Original entry on oeis.org
1, 2, 5, 22, 112, 623, 3664, 22405, 141002, 907228, 5940663, 39459873, 265228359, 1800608563, 12328843910, 85040632504, 590371016188, 4121775003434, 28921911896836, 203854515625194, 1442669458817907, 10247020573880520, 73024240955785936, 521973882076798493
Offset: 0
-
a(n) = sum(k=0, n, binomial(3*k+1, k)*binomial(k+1, n-k)/(3*k+1));
A381832
G.f. A(x) satisfies A(x) = C(x*A(x)^3) / (1 - x), where C(x) is the g.f. of A000108.
Original entry on oeis.org
1, 2, 10, 81, 796, 8616, 98973, 1184324, 14602486, 184219731, 2366543116, 30851212416, 407106050261, 5427274340091, 72986372975716, 988937692146346, 13487903251385562, 185022817888443780, 2551096865411701371, 35335463473311506321, 491444773227779518956, 6860346682881319595632
Offset: 0
-
a(n) = sum(k=0, n, binomial(5*k+1, k)*binomial(n+2*k, n-k)/(5*k+1));
Showing 1-3 of 3 results.