A366357
G.f. satisfies A(x) = 1/(1 - x) + x/A(x)^2.
Original entry on oeis.org
1, 2, -3, 19, -105, 690, -4781, 34708, -260189, 1999169, -15660175, 124596499, -1004110947, 8179379808, -67239070867, 557098881920, -4647368670949, 39001655222788, -329048378867467, 2789241880512899, -23743798316713367, 202894843070927860
Offset: 0
-
a(n) = (-1)^(n-1)*sum(k=0, n, binomial(3*k-1, k)*binomial(3*k-1, n-k)/(3*k-1));
A366454
G.f. A(x) satisfies A(x) = 1 + x + x/A(x)^(3/2).
Original entry on oeis.org
1, 2, -3, 12, -58, 312, -1794, 10794, -67113, 427800, -2780677, 18360504, -122809416, 830379966, -5666465445, 38974338126, -269915089194, 1880576960904, -13172489198859, 92705253700620, -655219698720486, 4648722344211012, -33096948925057703
Offset: 0
Cf.
A112478,
A364393,
A364407,
A364408,
A364409,
A366266,
A366267,
A366268,
A366452,
A366453,
A366455,
A366456.
-
a(n) = (-1)^(n-1)*sum(k=0, n, binomial(5*k/2-1, k)*binomial(n+3*k/2-2, n-k)/(5*k/2-1));
A366455
G.f. A(x) satisfies A(x) = 1 + x + x/A(x)^(5/2).
Original entry on oeis.org
1, 2, -5, 30, -215, 1710, -14516, 128830, -1180920, 11093830, -106245975, 1033454774, -10181848705, 101394979530, -1018972470275, 10320779179380, -105250097458410, 1079767027094630, -11136159773691830, 115395278542757580, -1200814926210284360
Offset: 0
Cf.
A112478,
A364393,
A364407,
A364408,
A364409,
A366266,
A366267,
A366268,
A366452,
A366453,
A366454,
A366456.
-
a(n) = (-1)^(n-1)*sum(k=0, n, binomial(7*k/2-1, k)*binomial(n+5*k/2-2, n-k)/(7*k/2-1));
A366456
G.f. A(x) satisfies A(x) = 1 + x + x/A(x)^(7/2).
Original entry on oeis.org
1, 2, -7, 56, -532, 5600, -62860, 737324, -8929726, 110811344, -1401640814, 18004922936, -234243536436, 3080152906096, -40870739065996, 546563064528906, -7358930622768977, 99672580921800656, -1357142384455626909, 18565841939010374736, -255054402946387767408
Offset: 0
Cf.
A112478,
A364393,
A364407,
A364408,
A364409,
A366266,
A366267,
A366268,
A366452,
A366453,
A366454,
A366455.
-
a(n) = (-1)^(n-1)*sum(k=0, n, binomial(9*k/2-1, k)*binomial(n+7*k/2-2, n-k)/(9*k/2-1));
A371893
G.f. A(x) satisfies A(x) = 1 + x/A(x)^2 * (1 + A(x)^4).
Original entry on oeis.org
1, 2, 0, 16, -32, 336, -1472, 10944, -63744, 441088, -2866688, 19772416, -134832128, 941381632, -6585720832, 46607831040, -331406262272, 2373110628352, -17072541007872, 123438375763968, -896088779128832, 6530356893777920, -47752086733717504
Offset: 0
-
a(n) = if(n==0, 1, (-1)^(n-1)*sum(k=0, n, binomial(n, k)*binomial(3*n-4*k-2, n-1))/n);
A371932
G.f. A(x) satisfies A(x) = 1 + x/A(x)^2 * (1 + A(x)^5).
Original entry on oeis.org
1, 2, 2, 26, 50, 706, 1650, 24282, 62370, 940610, 2554530, 39150810, 110311762, 1709993346, 4945525650, 77314273562, 228002115650, 3587763069826, 10741365151810, 169903043416730, 514833595840370, 8177978884039490, 25025386537586610
Offset: 0
-
a(n) = if(n==0, 1, (-1)^(n-1)*sum(k=0, n, binomial(n, k)*binomial(3*n-5*k-2, n-1))/n);