A370055
a(n) = 3*(3*n+2)!/(2*n+3)!.
Original entry on oeis.org
1, 3, 24, 330, 6552, 171360, 5581440, 218045520, 9945936000, 519177859200, 30535045632000, 1998518736614400, 144098325316915200, 11350405033583616000, 969837188805041356800, 89351761457237190912000, 8830056426362263572480000, 931769828125956695715840000
Offset: 0
A380511
Expansion of e.g.f. exp(x*G(x)^2) where G(x) = 1 + x*G(x)^3 is the g.f. of A001764.
Original entry on oeis.org
1, 1, 5, 55, 961, 23141, 711421, 26631235, 1175535425, 59786520841, 3442729157461, 221413508687471, 15730688410899265, 1223574846548300845, 103417508018836074701, 9437941200860641295611, 924934291227615821904001, 96881241931552168636182545, 10801002623361396194857667365
Offset: 0
-
a(n) = if(n==0, 1, 2*n!*sum(k=0, n-1, binomial(2*n+k, k)/((2*n+k)*(n-k-1)!)));
A375868
E.g.f. satisfies A(x) = exp( 2 * (exp(x*A(x)) - 1) ).
Original entry on oeis.org
1, 2, 14, 178, 3342, 83594, 2620998, 98968034, 4375295390, 221781470202, 12684194298998, 808136496137810, 56767509202678094, 4359070656483638762, 363283064756899367462, 32658326649544884611010, 3150270056733608259143422, 324571774149991316277596378
Offset: 0
-
a(n) = 2*sum(k=0, n, (2*n+2)^(k-1)*stirling(n, k, 2));
A380945
Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x)^2 * exp(-2*x) ).
Original entry on oeis.org
1, 4, 50, 1124, 37192, 1637232, 90278176, 5992556320, 465599728512, 41470892979200, 4167168740195584, 466428111222196224, 57556315795242096640, 7763511917730857967616, 1136484206117494859980800, 179453678311835212416585728, 30404317385796994658988752896
Offset: 0
-
a(n, q=2, r=2, s=2, t=0, u=1) = q*n!*sum(k=0, n, (r*n+(s-r)*k+q)^(k-1)*binomial((r*u+1)*n+((s-r)*u+t-1)*k+q*u-1, n-k)/k!);
Showing 1-4 of 4 results.