A366239
G.f. A(x) satisfies A(x) = 1 + x + x*(1 + x)^2*A(x)^3.
Original entry on oeis.org
1, 2, 8, 49, 329, 2401, 18452, 147140, 1206157, 10101011, 86047138, 743288984, 6495476548, 57321239999, 510104531479, 4572492374150, 41247768216331, 374175606700172, 3411195598361653, 31236732721224722, 287182875831208468, 2649838553953071239
Offset: 0
-
a(n) = sum(k=0, n, binomial(4*k+1, n-k)*binomial(3*k, k)/(2*k+1));
A366240
G.f. A(x) satisfies A(x) = 1 + x + x*(1 + x)^3*A(x)^3.
Original entry on oeis.org
1, 2, 9, 60, 432, 3378, 27792, 237122, 2079132, 18620709, 169614960, 1566540573, 14635978998, 138080055192, 1313596636812, 12587218990644, 121378106852988, 1176981533610012, 11469587139406515, 112265849283068877, 1103256200355696855
Offset: 0
-
a(n) = sum(k=0, n, binomial(5*k+1, n-k)*binomial(3*k, k)/(2*k+1));
A366241
G.f. A(x) satisfies A(x) = 1 + x + x*(1 + x)^4*A(x)^3.
Original entry on oeis.org
1, 2, 10, 72, 552, 4593, 40185, 364413, 3395217, 32305005, 312589540, 3066565720, 30430287693, 304907935707, 3080617021926, 31349533179726, 321038696185371, 3305935381202847, 34211612434972446, 355605873560512974, 3710978684625678870
Offset: 0
-
a(n) = sum(k=0, n, binomial(6*k+1, n-k)*binomial(3*k, k)/(2*k+1));
A379037
G.f. A(x) satisfies A(x) = ( (1 + x) * (1 + x*A(x)^(3/2)) )^2.
Original entry on oeis.org
1, 4, 18, 106, 689, 4782, 34707, 260190, 1999168, 15660176, 124596498, 1004110948, 8179379807, 67239070868, 557098881919, 4647368670950, 39001655222787, 329048378867468, 2789241880512898, 23743798316713368, 202894843070927859, 1739775692700850554
Offset: 0
-
a(n) = 2*sum(k=0, n, binomial(3*k+2, k)*binomial(3*k+2, n-k)/(3*k+2));
A379159
G.f. A(x) satisfies A(x) = (1 + x^3) * (1 + x*A(x)^3).
Original entry on oeis.org
1, 1, 3, 13, 59, 294, 1548, 8473, 47694, 274347, 1605553, 9529080, 57219636, 346989180, 2121996165, 13071868062, 81039237719, 505230120558, 3165528142389, 19922166970041, 125882558097870, 798300369383649, 5079196380442687, 32413550247722622, 207420591733202421
Offset: 0
-
a(n) = sum(k=0, n\3, binomial(3*n-9*k+1, k)*binomial(3*n-9*k+1, n-3*k)/(3*n-9*k+1));
A379160
G.f. A(x) satisfies A(x) = (1 + x^4) * (1 + x*A(x)^3).
Original entry on oeis.org
1, 1, 3, 12, 56, 277, 1449, 7872, 43978, 251049, 1457910, 8585724, 51152973, 307770236, 1867362978, 11412645576, 70194232585, 434157164246, 2698676669337, 16849393604484, 105621663128839, 664493496025485, 4194246946152171, 26553277765995984, 168567628890184974, 1072818569798746567
Offset: 0
-
a(n) = sum(k=0, n\4, binomial(3*n-12*k+1, k)*binomial(3*n-12*k+1, n-4*k)/(3*n-12*k+1));