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
A381778
G.f. A(x) satisfies A(x) = (1 + x*A(x)) * C(x*A(x)^2), where C(x) is the g.f. of A000108.
Original entry on oeis.org
1, 2, 9, 60, 474, 4105, 37681, 360122, 3545320, 35705553, 366126614, 3809497971, 40119258081, 426829897847, 4580629916321, 49527776299522, 539025763347730, 5900193301962178, 64913644702760248, 717433047054489969, 7961616716665723173, 88679610762886209459
Offset: 0
-
a(n) = sum(k=0, n, binomial(n+3*k+1, k)*binomial(n+k+1, n-k)/(n+3*k+1));
A381786
G.f. A(x) satisfies A(x) = (1 + x) * C(x*A(x)^3), where C(x) is the g.f. of A000108.
Original entry on oeis.org
1, 2, 9, 76, 744, 7986, 90836, 1075714, 13122656, 163769229, 2080985186, 26832199993, 350187469872, 4617094718728, 61406081813812, 822834184073768, 11098254270705028, 150555545320009712, 2052839917410937693, 28118478688846531072, 386727880988105218913, 5338557108832658927346
Offset: 0
-
a(n) = sum(k=0, n, binomial(5*k+1, k)*binomial(3*k+1, n-k)/(5*k+1));
Showing 1-3 of 3 results.