A381875
G.f. A(x) satisfies A(x) = C(x) / (1 - x*A(x))^2, where C(x) is the g.f. of A000108.
Original entry on oeis.org
1, 3, 13, 66, 368, 2185, 13570, 87147, 574241, 3861286, 26390591, 182798850, 1280387583, 9053335674, 64534088960, 463249047099, 3345832486407, 24296575830677, 177286818019264, 1299208549351640, 9557974679439901, 70563100013789595, 522608148884843970
Offset: 0
-
a(n) = sum(k=0, n, binomial(n+k+1, k)*binomial(3*n-3*k+1, n-k)/(n+k+1));
A381876
G.f. A(x) satisfies A(x) = C(x) / (1 - x*A(x))^3, where C(x) is the g.f. of A000108.
Original entry on oeis.org
1, 4, 23, 156, 1167, 9311, 77710, 670294, 5928183, 53467931, 489904745, 4547296624, 42667426369, 404044679434, 3856480309376, 37062228265769, 358330619946164, 3482936427997599, 34014454418349579, 333598711996924548, 3284326412065118717, 32446900771699499147
Offset: 0
-
a(n) = sum(k=0, n, binomial(n+k+1, k)*binomial(4*n-4*k+2, n-k)/(n+k+1));
A381861
G.f. A(x) satisfies A(x) = (1 + x*A(x))^4 * C(x), where C(x) is the g.f. of A000108.
Original entry on oeis.org
1, 5, 32, 231, 1797, 14715, 125064, 1093194, 9766783, 88793815, 818832674, 7640868924, 72014955566, 684551660324, 6555290711728, 63179148757584, 612376024087047, 5965515657187437, 58375460484257734, 573545171374958628, 5655759227878768987, 55957005428512022905
Offset: 0
-
a(n) = sum(k=0, n, binomial(n+k+1, k)*binomial(4*n-4*k+4, n-k)/(n+k+1));
Showing 1-3 of 3 results.