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));
A371517
G.f. A(x) satisfies A(x) = (1 + x*A(x) / (1-x))^4.
Original entry on oeis.org
1, 4, 26, 188, 1459, 11892, 100444, 871528, 7722557, 69590628, 635807180, 5876094308, 54836925779, 516029817620, 4891147100886, 46653935716492, 447490869463145, 4313492172957396, 41763413498670702, 405968522259130636, 3960526930400038404
Offset: 0
-
a(n) = 4*sum(k=0, n, binomial(n-1, n-k)*binomial(4*k+3, k)/(3*k+4));
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));
A371542
G.f. A(x) satisfies A(x) = (1 + x*A(x) / (1+x))^3.
Original entry on oeis.org
1, 3, 9, 34, 141, 621, 2849, 13467, 65127, 320686, 1602294, 8103087, 41397186, 213331026, 1107604764, 5788249329, 30422897664, 160717169622, 852894534042, 4544635033164, 24305345593290, 130423538829518, 701994030831654, 3788979493701069, 20503322609731348
Offset: 0
-
a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n-1, n-k)*binomial(3*k+3, k)/(k+1));
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));
Showing 1-5 of 5 results.