A381867
G.f. A(x) satisfies A(x) = C(x*A(x)) / (1 - x)^2, where C(x) is the g.f. of A000108.
Original entry on oeis.org
1, 3, 10, 44, 239, 1464, 9610, 65946, 466951, 3385259, 24999475, 187385168, 1421901090, 10901237530, 84312106160, 657031204068, 5153954345309, 40663760712441, 322478148002872, 2569086552458460, 20551321340065924, 165009872444132477, 1329352163579556971, 10742386009423170696
Offset: 0
-
a(n) = sum(k=0, n, binomial(3*k+1, k)*binomial(n+k+1, n-k)/(3*k+1));
A366215
G.f. A(x) satisfies A(x) = 1/(1 - x)^4 + x*(1 - x)^4*A(x)^4.
Original entry on oeis.org
1, 5, 26, 200, 1995, 22522, 272152, 3437280, 44806905, 598204475, 8137535934, 112382617018, 1571496538035, 22205618546014, 316570999534832, 4547819503936622, 65770112191659609, 956743348385310031, 13989838139093922658, 205511713513718581234
Offset: 0
-
a(n) = sum(k=0, n, binomial(n+7*k+3, n-k)*binomial(4*k, k)/(3*k+1));
A381944
G.f. A(x) satisfies A(x) = B(x*A(x)) / (1 - x)^3, where B(x) is the g.f. of A001764.
Original entry on oeis.org
1, 4, 16, 89, 655, 5592, 51594, 499159, 4990821, 51140527, 534152690, 5665496618, 60854697427, 660601882734, 7235771990454, 79870211543625, 887569516968685, 9921579561050637, 111487286796322366, 1258604967618419118, 14268057344239960863, 162358119295068686098
Offset: 0
-
a(n) = sum(k=0, n, binomial(4*k+1, k)*binomial(n+2*k+2, n-k)/(4*k+1));
A381947
G.f. A(x) satisfies A(x) = B(x*A(x)) / (1 - x)^3, where B(x) is the g.f. of A002293.
Original entry on oeis.org
1, 4, 17, 111, 1001, 10507, 118986, 1411789, 17307078, 217422098, 2784080234, 36201950786, 476725871599, 6344524132503, 85198695369123, 1152990558752089, 15708685673520617, 215287198676732925, 2965962577091646604, 41052101428818066604, 570583013508324005560
Offset: 0
-
a(n) = sum(k=0, n, binomial(5*k+1, k)*binomial(n+2*k+2, n-k)/(5*k+1));
Showing 1-4 of 4 results.