A365119
G.f. satisfies A(x) = (1 + x / (1 - x*A(x)))^3.
Original entry on oeis.org
1, 3, 6, 19, 69, 267, 1093, 4629, 20142, 89473, 404076, 1849746, 8563558, 40025574, 188612388, 895115942, 4274453904, 20523807009, 99025615998, 479874362583, 2334582421497, 11398055887003, 55828060595832, 274254002718255, 1350907899813921, 6670789629569022
Offset: 0
-
a(n, s=1, t=3) = sum(k=0, n, binomial(t*(n-k+1), k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));
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));
A365120
G.f. A(x) satisfies A(x) = (1 + x / (1 - x*A(x))^2)^2.
Original entry on oeis.org
1, 2, 5, 18, 70, 294, 1291, 5864, 27314, 129766, 626367, 3063096, 15143562, 75563924, 380062186, 1924840480, 9807649900, 50241194250, 258597717591, 1336730670244, 6936403057274, 36119232561000, 188677598254078, 988464846388710, 5192270327405662
Offset: 0
-
a(n, s=2, t=2) = sum(k=0, n, binomial(t*(n-k+1), k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));
A371613
G.f. satisfies A(x) = ( 1 + x / (1 - x*A(x)^3) )^2.
Original entry on oeis.org
1, 2, 3, 16, 83, 460, 2767, 17210, 110308, 723624, 4832363, 32747106, 224619408, 1556484636, 10879744696, 76621739626, 543159825499, 3872610857558, 27752175177823, 199787917082084, 1444171829169939, 10477887409768628, 76275565075016394
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(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));
A378801
G.f. A(x) satisfies A(x) = ( 1 + x/(1 - x*A(x)^(2/3)) )^3.
Original entry on oeis.org
1, 3, 6, 16, 48, 153, 511, 1761, 6219, 22383, 81804, 302766, 1132475, 4274166, 16256685, 62249167, 239772510, 928398831, 3611539758, 14107963848, 55318781982, 217652858539, 859027927911, 3400055112777, 13492710661658, 53673238384560, 213984657134418
Offset: 0
-
a(n, r=3, s=1, t=0, 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));
A378732
G.f. A(x) satisfies A(x) = ( 1 + x / (1 - x*A(x)) )^4.
Original entry on oeis.org
1, 4, 10, 36, 155, 704, 3384, 16844, 86097, 449344, 2384170, 12822556, 69743953, 382982940, 2120323014, 11822279232, 66327376437, 374162700460, 2120999728610, 12075668658000, 69021358842795, 395909382981572, 2278286453089574, 13149207655326372, 76096242994616990
Offset: 0
-
a(n, r=4, 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));
Showing 1-6 of 6 results.