A364864
G.f. A(x) satisfies A(x) = 1 + x*A(x)^3 / (1 + x*A(x)^3).
Original entry on oeis.org
1, 1, 2, 4, 6, -1, -58, -304, -1090, -2876, -4216, 9244, 106746, 529962, 1874628, 4669760, 4309742, -35179252, -277928680, -1269921008, -4214431912, -9197175241, 30113526, 128659598896, 822227670866, 3453484223084, 10519017940952, 18490932535144
Offset: 0
-
a(n) = sum(k=0, n, (-1)^k*2^(n-k)*binomial(n, k)*binomial(3*n+k+1, n)/(3*n+k+1));
A364738
G.f. satisfies A(x) = 1 + x*A(x) / (1 + x*A(x)^5).
Original entry on oeis.org
1, 1, 0, -5, -10, 40, 245, -26, -4375, -11410, 53040, 377850, -12320, -7988194, -23011625, 106662595, 824671575, 64095550, -18490968680, -57052839001, 254513058375, 2098532784575, 419490572800, -48205987947600, -157458581103395, 666628546612606, 5824573247731250
Offset: 0
-
a(n) = if(n==0, 1, sum(k=0, n-1, (-1)^k*binomial(n, k)*binomial(n+4*k, n-1-k))/n);
A378892
G.f. A(x) satisfies A(x) = 1 + x*A(x)^6/(1 + x*A(x)^3).
Original entry on oeis.org
1, 1, 5, 37, 322, 3067, 30951, 325171, 3519038, 38959997, 439177850, 5023590609, 58163050071, 680308820750, 8026782091957, 95419476630100, 1141762194395927, 13740910664096101, 166216043531507231, 2019807368837970964, 24644779751103948475, 301818330734940817283
Offset: 0
-
a(n, r=1, s=-1, t=6, u=3) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));
A364735
G.f. satisfies A(x) = 1 + x*A(x) / (1 + x*A(x)^2).
Original entry on oeis.org
1, 1, 0, -2, -1, 8, 10, -37, -84, 168, 660, -624, -4950, 583, 35464, 23166, -240513, -359008, 1511640, 3898100, -8387664, -36522256, 35444728, 311764768, -25659766, -2466384737, -1793133360, 18077558170, 28951038285, -120750295320, -330486900870
Offset: 0
-
a(n) = if(n==0, 1, sum(k=0, n-1, (-1)^k*binomial(n, k)*binomial(n+k, n-1-k))/n);
A364737
G.f. satisfies A(x) = 1 + x*A(x) / (1 + x*A(x)^4).
Original entry on oeis.org
1, 1, 0, -4, -6, 28, 119, -116, -1820, -2128, 22212, 79877, -172700, -1652728, -857428, 25387284, 71506309, -268817888, -1838702048, 449975584, 33164610276, 68575577309, -429542625096, -2221814345660, 2539462697398, 46048818685880, 61721413191310
Offset: 0
-
a(n) = if(n==0, 1, sum(k=0, n-1, (-1)^k*binomial(n, k)*binomial(n+3*k, n-1-k))/n);
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));
Showing 1-6 of 6 results.