A365086
G.f. satisfies A(x) = 1 + x*A(x) / (1 + x*A(x))^3.
Original entry on oeis.org
1, 1, -2, -2, 15, -4, -122, 204, 903, -3374, -4635, 43539, -13233, -475123, 873392, 4244591, -16906773, -24952174, 244162840, -74520792, -2901715074, 5483226036, 27740164293, -112969486284, -172903931727, 1714556657881, -513739179725, -21235809823325
Offset: 0
-
a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n, k)*binomial(n+2*k-1, n-k)/(n-k+1));
A365087
G.f. satisfies A(x) = 1 + x*A(x) / (1 + x*A(x))^4.
Original entry on oeis.org
1, 1, -3, -1, 29, -44, -265, 1114, 1369, -19076, 20388, 250977, -875281, -2116594, 19136754, -7765108, -306092007, 830209808, 3388957208, -22266676364, -8185922076, 413223401045, -814031607979, -5513566634947, 27558060911119, 35395095404776
Offset: 0
-
a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n, k)*binomial(n+3*k-1, n-k)/(n-k+1));
A365088
G.f. satisfies A(x) = 1 + x*A(x) / (1 + x*A(x))^5.
Original entry on oeis.org
1, 1, -4, 1, 46, -129, -405, 3319, -1617, -59258, 199541, 642170, -6038395, 3886091, 119884973, -440626784, -1367688245, 14055527190, -11043763380, -290488387366, 1137260033731, 3336325340735, -36966844508130, 34098313310315, 776097820004580
Offset: 0
-
a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n, k)*binomial(n+4*k-1, n-k)/(n-k+1));
A365109
G.f. satisfies A(x) = 1 + x / (1 + x*A(x))^2.
Original entry on oeis.org
1, 1, -2, 1, 6, -18, 8, 89, -266, 62, 1684, -4710, -220, 35648, -91236, -34871, 803302, -1856874, -1448844, 18809694, -38816620, -48910700, 451491680, -820626294, -1522994404, 11015923292, -17319046712, -45512957516, 271664145264, -359911736252, -1327355044924
Offset: 0
-
a(n, s=2) = sum(k=0, n, (-1)^(n-k)*binomial(n-k+1, k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));
Showing 1-4 of 4 results.