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));
A371516
G.f. A(x) satisfies A(x) = (1 + x*A(x) / (1-x))^3.
Original entry on oeis.org
1, 3, 15, 82, 477, 2901, 18235, 117555, 773085, 5166478, 34987170, 239570655, 1655933060, 11538839130, 80971109712, 571702698185, 4058556404958, 28951715755830, 207424064434502, 1491898838023884, 10768487956456506, 77977009814421534, 566310026687320290
Offset: 0
-
a(n) = 3*sum(k=0, n, binomial(n-1, n-k)*binomial(3*k+2, k)/(2*k+3));
A371520
G.f. A(x) satisfies A(x) = (1 + x*A(x) / (1-x))^5.
Original entry on oeis.org
1, 5, 40, 360, 3495, 35726, 378965, 4133080, 46059020, 522196465, 6004261226, 69849651025, 820651943130, 9723556336780, 116056250171385, 1394082307995626, 16840510019954835, 204453614350921540, 2493311080293185200, 30528431677508637205, 375155454309681439001
Offset: 0
-
a(n) = 5*sum(k=0, n, binomial(n-1, n-k)*binomial(5*k+4, k)/(4*k+5));
A371518
G.f. A(x) satisfies A(x) = (1 + x*A(x)^2 / (1-x))^2.
Original entry on oeis.org
1, 2, 11, 72, 525, 4104, 33647, 285526, 2486809, 22103726, 199697284, 1828472914, 16929944932, 158246198836, 1491210732346, 14151603542612, 135130396860130, 1297381593071890, 12516650939119421, 121281286192026308, 1179769340479567499
Offset: 0
-
a(n) = 2*sum(k=0, n, binomial(n-1, n-k)*binomial(4*k+1, k)/(3*k+2));
A370695
G.f. A(x) satisfies A(x) = (1 + x*A(x)^(3/4) / (1-x))^4.
Original entry on oeis.org
1, 4, 22, 128, 777, 4872, 31330, 205560, 1370868, 9266104, 63343006, 437183260, 3042337215, 21323543252, 150395596016, 1066637271424, 7602188660799, 54422262148632, 391146728466980, 2821396586367568, 20417766975784066, 148200184917042112
Offset: 0
-
A370695 := proc(n)
4*add(binomial(n-1,n-k)*binomial(3*k+4,k)/(3*k+4),k=0..n) ;
end proc:
seq(A370695(n),n=0..80) ; #R. J. Mathar, Oct 24 2024
-
a(n) = 4*sum(k=0, n, binomial(n-1, n-k)*binomial(3*k+4, k)/(3*k+4));
A371543
G.f. A(x) satisfies A(x) = (1 + x*A(x) / (1+x))^4.
Original entry on oeis.org
1, 4, 18, 100, 611, 3964, 26796, 186664, 1330541, 9657748, 71138964, 530417668, 3995461515, 30359913132, 232434013174, 1791205897652, 13883372595753, 108159238126644, 846472588860134, 6651825146945508, 52465622957295300, 415208597109815172
Offset: 0
-
a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n-1, n-k)*binomial(4*k+4, k)/(k+1));
Showing 1-6 of 6 results.