A379246
G.f. A(x) satisfies A(x) = ( (1 + x*A(x)^3)/(1 - x*A(x)) )^3.
Original entry on oeis.org
1, 6, 90, 1838, 43362, 1111878, 30101786, 846703950, 24501770370, 724733787206, 21813611057562, 665947742487342, 20571682188676450, 641823879285627654, 20195381326042866138, 640146274715559742670, 20421757641058980395010, 655181707585675667750790, 21125606434257067959841242
Offset: 0
-
a(n) = sum(k=0, n, binomial(3*n+6*k+3, k)*binomial(4*n+5*k+2, n-k)/(n+2*k+1));
A379254
G.f. A(x) satisfies A(x) = ( (1 + x*A(x))/(1 - x*A(x)^2) )^3.
Original entry on oeis.org
1, 6, 72, 1136, 20496, 400176, 8230592, 175643712, 3852905472, 86338960640, 1967950718976, 45483461999616, 1063433350498304, 25107661327202304, 597766180153565184, 14335020154675867648, 345948883288769740800, 8395511682729703931904
Offset: 0
-
a(n) = sum(k=0, n, binomial(3*n+4*k+2, k)*binomial(3*n+3*k+3, n-k)/(n+k+1));
A379255
G.f. A(x) satisfies A(x) = ( (1 + x*A(x))/(1 - x*A(x)^3) )^3.
Original entry on oeis.org
1, 6, 90, 1910, 47250, 1274406, 36344906, 1077809718, 32899427106, 1026823733702, 32619190553274, 1051205539768566, 34282637873690290, 1129326395659189734, 37522172645425790634, 1255954522404101871286, 42312438228338307500610, 1433621819994034883749254
Offset: 0
-
a(n) = sum(k=0, n, binomial(3*n+7*k+2, k)*binomial(3*n+6*k+3, n-k)/(n+2*k+1));
A378840
G.f. A(x) satisfies A(x) = ( 1 + x * A(x)^(4/3) * (1 + A(x)^(1/3)) )^3.
Original entry on oeis.org
1, 6, 66, 902, 13794, 225990, 3878946, 68854278, 1253647938, 23283474310, 439394508162, 8401507608966, 162413310158626, 3169029168475206, 62330703549363810, 1234503404283308038, 24599422679682518658, 492824963618477891334, 9920626149798702401730
Offset: 0
-
a(n, r=3, t=4, u=1) = r*sum(k=0, n, binomial(n, k)*binomial(t*n+u*k+r, n)/(t*n+u*k+r));