A378952
G.f. A(x) satisfies A(x) = ( 1 + x*A(x)^2/(1 + x*A(x)^(4/3)) )^3.
Original entry on oeis.org
1, 3, 18, 139, 1218, 11511, 114398, 1178421, 12469626, 134734092, 1480317468, 16487870031, 185744716414, 2112756042468, 24230663513604, 279889210974003, 3253295301115290, 38023971948455859, 446603044829013514, 5268557500949993964, 62398899992129490756
Offset: 0
-
a(n, r=3, s=-1, t=6, u=4) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));
A370891
G.f. satisfies A(x) = ( 1 + x * A(x)^(1/4) * (1 + A(x)^(3/4)) )^2.
Original entry on oeis.org
1, 4, 14, 52, 205, 844, 3588, 15632, 69434, 313264, 1431650, 6613732, 30834548, 144895284, 685566370, 3263309844, 15616322995, 75085908112, 362563417968, 1757412095456, 8548129677400, 41710100368160, 204110896990686, 1001480947876276, 4925833177966164
Offset: 0
-
a(n) = 2*sum(k=0, n, binomial(n, k)*binomial(n/2+3*k/2+2, n)/(n/2+3*k/2+2));
A371725
G.f. satisfies A(x) = ( 1 + x * A(x)^(1/5) * (1 + A(x)) )^(5/2).
Original entry on oeis.org
1, 5, 25, 145, 925, 6266, 44245, 322075, 2399725, 18211775, 140285018, 1093997085, 8620125925, 68523526635, 548867710575, 4425604018075, 35892727867805, 292604563615625, 2396375011877275, 19707111724556025, 162671328783723678, 1347313142469049275
Offset: 0
-
a(n) = sum(k=0, n, binomial(n, k)*binomial(n/2+5*k/2+5/2, n)/(n/5+k+1));
A378951
G.f. A(x) satisfies A(x) = ( 1 + x*A(x)^(5/3)/(1 + x*A(x)) )^3.
Original entry on oeis.org
1, 3, 15, 94, 663, 5025, 39970, 329145, 2782095, 23999078, 210427869, 1869908364, 16802935370, 152425394958, 1393972037301, 12838326815582, 118970843349711, 1108503805898190, 10378559702646846, 97593299922016224, 921294705307189029
Offset: 0
-
a(n, r=3, s=-1, t=5, 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));
Showing 1-4 of 4 results.