A365120
G.f. A(x) satisfies A(x) = (1 + x / (1 - x*A(x))^2)^2.
Original entry on oeis.org
1, 2, 5, 18, 70, 294, 1291, 5864, 27314, 129766, 626367, 3063096, 15143562, 75563924, 380062186, 1924840480, 9807649900, 50241194250, 258597717591, 1336730670244, 6936403057274, 36119232561000, 188677598254078, 988464846388710, 5192270327405662
Offset: 0
-
a(n, s=2, t=2) = sum(k=0, n, binomial(t*(n-k+1), k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));
A365124
G.f. satisfies A(x) = (1 + x / (1 - x*A(x))^4)^4.
Original entry on oeis.org
1, 4, 22, 156, 1209, 10020, 86724, 775044, 7096652, 66232980, 627749066, 6025752664, 58459917618, 572315274540, 5646713239840, 56091780016288, 560513824012020, 5630664768126388, 56829055796539462, 575981263878482204, 5859952654335118851
Offset: 0
-
a(n, s=4, t=4) = sum(k=0, n, binomial(t*(n-k+1), k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));
A378733
G.f. A(x) satisfies A(x) = 1 + x / (1 - x*A(x)^2)^4.
Original entry on oeis.org
1, 1, 4, 18, 96, 551, 3332, 20906, 134820, 888151, 5951096, 40432550, 277892604, 1928668910, 13497833600, 95150192558, 674993798716, 4815149310441, 34519885929860, 248571425473698, 1797058507267104, 13038781500215352, 94914559729835580, 692987915940266152
Offset: 0
-
A378733 := proc(n)
add(binomial(2*(n-k)+1, k)*binomial(n+3*k-1, n-k)/(2*(n-k)+1),k=0..n) ;
end proc:
seq(A378733(n),n=0..80) ; # R. J. Mathar, Dec 15 2024
-
a(n, r=1, s=4, t=0, u=2) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));
Showing 1-3 of 3 results.