A371612
G.f. satisfies A(x) = ( 1 + x / (1 - x*A(x)^2) )^2.
Original entry on oeis.org
1, 2, 3, 12, 49, 218, 1037, 5106, 25909, 134410, 709691, 3801498, 20606654, 112828202, 623087675, 3466539248, 19411070496, 109313442562, 618713495451, 3517737628368, 20081523836403, 115058714898196, 661432784830204, 3813891082337178, 22052422636145522
Offset: 0
-
a(n, r=2, s=1, t=0, u=4) = 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));
A371615
G.f. satisfies A(x) = ( 1 + x / (1 - x*A(x)^3)^2 )^2.
Original entry on oeis.org
1, 2, 5, 34, 222, 1622, 12559, 100904, 835322, 7070574, 60922335, 532566850, 4711614912, 42106192680, 379544358032, 3446755447528, 31504896429042, 289619348156494, 2675953520657839, 24836797229730316, 231461661673958896, 2165002179076830442
Offset: 0
-
a(n, r=2, s=2, t=0, u=6) = 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));
A371617
G.f. satisfies A(x) = ( 1 + x / (1 - x*A(x)^3)^3 )^2.
Original entry on oeis.org
1, 2, 7, 54, 419, 3644, 33366, 317672, 3113559, 31200060, 318219653, 3292546660, 34475311605, 364621943538, 3889561661610, 41799988930926, 452126713579192, 4918321519144206, 53773399008883695, 590578523863692086, 6512515698908748358
Offset: 0
-
a(n, r=2, s=3, t=0, u=6) = 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));
A371608
G.f. satisfies A(x) = ( 1 + x * (1 + x*A(x)^3) )^2.
Original entry on oeis.org
1, 2, 3, 14, 55, 226, 1042, 4840, 23103, 113118, 561568, 2826550, 14392534, 73967650, 383271596, 2000096144, 10502029735, 55446004880, 294155761676, 1567371462762, 8384300275607, 45009106969022, 242400290365756, 1309314066314354, 7091306989205453
Offset: 0
-
a(n, r=2, s=1, t=0, u=6) = 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.