A365114
G.f. satisfies A(x) = 1 + x / (1 - x*A(x))^4.
Original entry on oeis.org
1, 1, 4, 14, 56, 241, 1080, 4998, 23704, 114588, 562552, 2797138, 14057140, 71288385, 364360204, 1874960408, 9706035408, 50510552881, 264096980192, 1386676113360, 7308650513232, 38654087828310, 205076534841112, 1091144400876394, 5820924498941668
Offset: 0
-
a(n, s=4) = sum(k=0, n, binomial(n-k+1, k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));
A367233
G.f. satisfies A(x) = 1 + x*A(x)^3 / (1 - x*A(x))^3.
Original entry on oeis.org
1, 1, 6, 39, 284, 2223, 18267, 155445, 1358073, 12111306, 109802183, 1009001571, 9376972698, 87978198364, 832223905371, 7928413841673, 76002832317437, 732578811761670, 7095717550127526, 69029297500888522, 674181392461483212, 6607910786529613248
Offset: 0
-
a(n, s=3, 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));
A371616
G.f. satisfies A(x) = 1 + x / (1 - x*A(x)^3)^3.
Original entry on oeis.org
1, 1, 3, 15, 82, 495, 3147, 20812, 141621, 985287, 6976369, 50108232, 364202415, 2673756449, 19797659586, 147677816532, 1108711280376, 8371222635096, 63525564996093, 484243596619753, 3706268752629237, 28470703720193010, 219432896755734137
Offset: 0
-
a(n, r=1, s=3, t=0, u=3) = 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));
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));
A365122
G.f. A(x) satisfies A(x) = (1 + x / (1 - x*A(x))^3)^3.
Original entry on oeis.org
1, 3, 12, 64, 372, 2319, 15105, 101649, 701073, 4929657, 35207220, 254690517, 1862325262, 13742311074, 102204992352, 765328009950, 5765316776550, 43661497944861, 332217854059362, 2538540859615095, 19471592691620310, 149871698475060433, 1157188723053901449
Offset: 0
-
a(n, s=3, t=3) = sum(k=0, n, binomial(t*(n-k+1), k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));
Showing 1-5 of 5 results.