A367233
G.f. satisfies A(x) = 1 + x*A(x)^3 / (1 - x*A(x))^3.
Original entry on oeis.org
1, 1, 6, 39, 284, 2223, 18267, 155445, 1358073, 12111306, 109802183, 1009001571, 9376972698, 87978198364, 832223905371, 7928413841673, 76002832317437, 732578811761670, 7095717550127526, 69029297500888522, 674181392461483212, 6607910786529613248
Offset: 0
-
a(n, s=3, t=3, u=1) = sum(k=0, n, binomial(t*k+u*(n-k)+1, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+1));
A365151
G.f. satisfies A(x) = ( 1 + x*A(x)^2 / (1 - x*A(x))^3 )^2.
Original entry on oeis.org
1, 2, 15, 130, 1263, 13158, 143704, 1623766, 18824931, 222670678, 2676674916, 32604377358, 401567277063, 4992440157784, 62569729324806, 789679959184598, 10027614784648750, 128024712530277906, 1642407060905790817, 21161202394988206098
Offset: 0
-
a(n, s=3, t=2) = sum(k=0, n, binomial(t*(n+k+1), k)*binomial(n+(s-1)*k-1, n-k)/(n+k+1));
A365152
G.f. satisfies A(x) = ( 1 + x*A(x)^2 / (1 - x*A(x))^3 )^3.
Original entry on oeis.org
1, 3, 30, 361, 4887, 71064, 1084338, 17127921, 277691055, 4594624095, 77271742056, 1317037554924, 22699836814548, 394961294853852, 6928051002350154, 122384261274499665, 2175295243858562031, 38875484049230706129, 698131263508514451678
Offset: 0
-
a(n, s=3, t=3) = sum(k=0, n, binomial(t*(n+k+1), k)*binomial(n+(s-1)*k-1, n-k)/(n+k+1));
A367234
G.f. satisfies A(x) = 1 + x*A(x)^2 / (1 - x*A(x))^4.
Original entry on oeis.org
1, 1, 6, 35, 226, 1561, 11276, 84150, 643730, 5021038, 39781858, 319282210, 2590312872, 21208628405, 175024439504, 1454329099044, 12157356271998, 102170610282040, 862721635191860, 7315768816166027, 62274763166575410, 531950072655682896, 4558282056420235664
Offset: 0
-
a(n, s=4, t=2, u=1) = sum(k=0, n, binomial(t*k+u*(n-k)+1, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+1));
A378566
a(n) = Sum_{k=0..n} binomial(n+k-1,k) * binomial(n+2*k-1,n-k).
Original entry on oeis.org
1, 1, 9, 64, 465, 3456, 26082, 199060, 1532313, 11875015, 92528414, 724187982, 5689127886, 44834549501, 354289977750, 2806262293824, 22273793685609, 177113634045858, 1410633764438967, 11251419724586850, 89860413370562730, 718528004169570925
Offset: 0
-
a(n) = sum(k=0, n, binomial(n+k-1, k)*binomial(n+2*k-1, n-k));
A367281
G.f. satisfies A(x) = 1 + x*A(x)^2 / (1 - x*A(x)^3)^3.
Original entry on oeis.org
1, 1, 5, 32, 237, 1906, 16179, 142665, 1294115, 11998349, 113194205, 1083131419, 10486939473, 102548233212, 1011333385507, 10047289999536, 100458873883179, 1010138430187185, 10208244014494347, 103625607305637693, 1056166710786300973
Offset: 0
-
a(n, s=3, t=2, u=3) = sum(k=0, n, binomial(t*k+u*(n-k)+1, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+1));
Showing 1-6 of 6 results.