A365113
G.f. satisfies A(x) = 1 + x / (1 - x*A(x))^3.
Original entry on oeis.org
1, 1, 3, 9, 31, 114, 438, 1739, 7077, 29364, 123756, 528324, 2279868, 9928679, 43580301, 192601419, 856317717, 3827501985, 17188943523, 77521747638, 350959738842, 1594390493067, 7266093316649, 33209221327752, 152182572790008, 699083290518817, 3218624408121555
Offset: 0
-
a(n, s=3) = sum(k=0, n, binomial(n-k+1, k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));
A365123
G.f. satisfies A(x) = (1 + x / (1 - x*A(x))^4)^2.
Original entry on oeis.org
1, 2, 9, 44, 244, 1438, 8858, 56340, 367160, 2438934, 16453015, 112411836, 776258588, 5409237100, 37988571802, 268606426836, 1910584687932, 13661702623498, 98148312810335, 708092115326436, 5127976641997944, 37264674894021280, 271650189521574734
Offset: 0
-
a(n, s=4, t=2) = sum(k=0, n, binomial(t*(n-k+1), k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));
A367235
G.f. satisfies A(x) = 1 + x*A(x)^3 / (1 - x*A(x))^4.
Original entry on oeis.org
1, 1, 7, 50, 399, 3422, 30798, 286974, 2744947, 26798010, 265945022, 2674970684, 27209385886, 279412999031, 2892787737002, 30161921520976, 316440334960563, 3338105334701396, 35385133077851602, 376732207920371784, 4026682585718602014
Offset: 0
-
a(n, s=4, t=3, u=1) = sum(k=0, n, binomial(t*k+u*(n-k)+1, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+1));
A365115
G.f. satisfies A(x) = 1 + x / (1 - x*A(x))^5.
Original entry on oeis.org
1, 1, 5, 20, 90, 440, 2236, 11720, 62960, 344690, 1916170, 10787762, 61380770, 352410760, 2039099640, 11878519460, 69608606348, 410056995475, 2426936098575, 14424334077975, 86055337016695, 515170271387970, 3093724519080210, 18631778892165080
Offset: 0
-
a(n, s=5) = sum(k=0, n, binomial(n-k+1, k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));
A367234
G.f. satisfies A(x) = 1 + x*A(x)^2 / (1 - x*A(x))^4.
Original entry on oeis.org
1, 1, 6, 35, 226, 1561, 11276, 84150, 643730, 5021038, 39781858, 319282210, 2590312872, 21208628405, 175024439504, 1454329099044, 12157356271998, 102170610282040, 862721635191860, 7315768816166027, 62274763166575410, 531950072655682896, 4558282056420235664
Offset: 0
-
a(n, s=4, t=2, u=1) = sum(k=0, n, binomial(t*k+u*(n-k)+1, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+1));
A365124
G.f. satisfies A(x) = (1 + x / (1 - x*A(x))^4)^4.
Original entry on oeis.org
1, 4, 22, 156, 1209, 10020, 86724, 775044, 7096652, 66232980, 627749066, 6025752664, 58459917618, 572315274540, 5646713239840, 56091780016288, 560513824012020, 5630664768126388, 56829055796539462, 575981263878482204, 5859952654335118851
Offset: 0
-
a(n, s=4, t=4) = sum(k=0, n, binomial(t*(n-k+1), k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));
Showing 1-6 of 6 results.