A371521
G.f. A(x) satisfies A(x) = (1 + x*A(x) / (1-x))^6.
Original entry on oeis.org
1, 6, 57, 614, 7158, 88002, 1123689, 14760024, 198172050, 2707560544, 37522666803, 526190125308, 7452866846847, 106465245105972, 1532129408941797, 22191180837313808, 323243244688652943, 4732225866305323686, 69591395772704207770, 1027547992261749954798
Offset: 0
-
a(n) = 6*sum(k=0, n, binomial(n-1, n-k)*binomial(6*k+5, k)/(5*k+6));
A371523
G.f. A(x) satisfies A(x) = (1 + x*A(x)^3 / (1-x))^2.
Original entry on oeis.org
1, 2, 15, 142, 1533, 17924, 220936, 2827218, 37202580, 500228562, 6842899886, 94931338876, 1332438761910, 18887047322030, 269986427261981, 3887654399820062, 56337997080499605, 821021578186212094, 12024687038651388155, 176900548019426869808, 2612917215947948178941
Offset: 0
-
a(n) = 2*sum(k=0, n, binomial(n-1, n-k)*binomial(6*k+1, k)/(5*k+2));
A371379
G.f. A(x) satisfies A(x) = (1 + x*A(x)^(3/2) / (1-x))^4.
Original entry on oeis.org
1, 4, 34, 344, 3859, 46240, 579722, 7511272, 99782617, 1351784792, 18604380884, 259395030992, 3656180724752, 52011780756632, 745799171500502, 10768038899631476, 156414710103922340, 2284233700081510820, 33517461646190624690, 493917761019513208800
Offset: 0
-
a(n) = 4*sum(k=0, n, binomial(n-1, n-k)*binomial(6*k+3, k)/(5*k+4));
A371522
G.f. A(x) satisfies A(x) = (1 + x*A(x)^2 / (1-x))^3.
Original entry on oeis.org
1, 3, 24, 235, 2586, 30603, 380359, 4896753, 64731747, 873539236, 11984536632, 166661420814, 2343950447112, 33282048811530, 476462982915993, 6869620848003570, 99663539644072305, 1453861111238442363, 21312207036239313936, 313783619269186619589
Offset: 0
-
a(n) = 3*sum(k=0, n, binomial(n-1, n-k)*binomial(6*k+2, k)/(5*k+3));
A371540
G.f. A(x) satisfies A(x) = 1 / (1 - x*A(x) / (1+x))^5.
Original entry on oeis.org
1, 5, 35, 310, 3055, 32151, 353755, 4019825, 46808750, 555621400, 6698027100, 81779512155, 1009194553315, 12567338972700, 157725047958100, 1992990741398625, 25333585976926275, 323725357496659565, 4156196637610760235, 53585106340408250725, 693491493195479127175
Offset: 0
-
a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n-1, n-k)*binomial(6*k+4, k)/(k+1));
Showing 1-5 of 5 results.