A371581
G.f. satisfies A(x) = ( 1 + x*A(x)^(5/2) / (1 - x*A(x)) )^2.
Original entry on oeis.org
1, 2, 13, 108, 1018, 10352, 110724, 1227752, 13986369, 162708728, 1924866345, 23085868814, 280060995369, 3430479393210, 42369377446083, 527064922683286, 6597825455023465, 83050276697808472, 1050551595788997356, 13347641275527720048, 170259412138463630535
Offset: 0
-
a(n, r=2, s=1, t=5, u=2) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));
A372164
E.g.f. A(x) satisfies A(x) = exp( 2 * x * A(x)^(5/2) * (1 + x * A(x)) ).
Original entry on oeis.org
1, 2, 28, 746, 30344, 1668762, 116000044, 9760665434, 964821252528, 109605653026802, 14072453189095124, 2015280776336738418, 318501367837803765640, 55067060355743834423690, 10339257411931121356190652, 2095051036885575920328492938, 455698493422117961626699815776
Offset: 0
-
a(n, r=2, s=1, t=5, u=2) = r*n!*sum(k=0, n, (t*k+u*(n-k)+r)^(k-1)*binomial(s*k, n-k)/k!);
A371575
G.f. satisfies A(x) = ( 1 + x*A(x)^3 * (1 + x*A(x)) )^2.
Original entry on oeis.org
1, 2, 15, 144, 1587, 18942, 238301, 3111788, 41779164, 573127760, 7998164674, 113189243386, 1620583793262, 23431706243230, 341654376602948, 5017986762425680, 74170837061591036, 1102479579201183898, 16469074050937364044, 247115476148847822586
Offset: 0
-
a(n, r=2, s=1, t=6, u=2) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));
A371579
G.f. satisfies A(x) = ( 1 + x*A(x)^(5/2) * (1 + x*A(x))^2 )^2.
Original entry on oeis.org
1, 2, 15, 134, 1367, 15032, 173836, 2083806, 25660383, 322666882, 4125822703, 53482104104, 701223274308, 9283066366256, 123912439591104, 1665895096499278, 22537232138264271, 306586712969384678, 4191205834907493725, 57548344232637695030, 793311718924341065567
Offset: 0
-
a(n, r=2, s=2, t=5, u=2) = 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.