A372005
G.f. A(x) satisfies A(x) = ( 1 + 16*x*A(x)*(1 + x*A(x)) )^(1/4).
Original entry on oeis.org
1, 4, -4, 0, 136, -1152, 5152, 0, -230560, 2267136, -11355008, 0, 594412800, -6184304640, 32458736640, 0, -1828185954816, 19583341166592, -105435193825280, 0, 6195266435870720, -67554137604096000, 369569533686562816, 0, -22322916873246359552, 246346071588005216256
Offset: 0
-
a(n) = sum(k=0, n, 16^k*binomial(n/4+1/4, k)*binomial(k, n-k))/(n+1);
A372019
G.f. A(x) satisfies A(x) = ( 1 + 9*x*A(x)/(1 - x*A(x)) )^(1/3).
Original entry on oeis.org
1, 3, 3, 3, 30, 57, 84, 867, 1893, 3162, 33132, 76953, 136812, 1446204, 3478764, 6420387, 68260134, 167946159, 317782524, 3392340186, 8479140510, 16332164868, 174873206424, 442212416121, 863222622780, 9264327739716, 23637757714788, 46624054987452
Offset: 0
-
A371019 := proc(n)
add(9^k*binomial((n+1)/3,k)*binomial(n-1,k-1),k=0..n) ;
%/(n+1) ;
end proc:
seq(A371019(n),n=0..60) ; # R. J. Mathar, Apr 22 2024
-
a(n) = sum(k=0, n, 9^k*binomial(n/3+1/3, k)*binomial(n-1, n-k))/(n+1);
A372006
G.f. A(x) satisfies A(x) = ( 1 + 25*x*A(x)*(1 + x*A(x)) )^(1/5).
Original entry on oeis.org
1, 5, -20, 100, 0, -9625, 169875, -1933125, 14025625, 0, -2065744375, 41575056250, -523670743750, 4119815531250, 0, -684944792812500, 14442398472421875, -189324209836328125, 1541918426557031250, 0, -271410262779871875000, 5860693797318871093750
Offset: 0
-
a(n) = sum(k=0, n, 25^k*binomial(n/5+1/5, k)*binomial(k, n-k))/(n+1);
A372091
G.f. A(x) satisfies A(x) = 1/( 1 - 9*x*A(x)*(1 + x*A(x)) )^(1/3).
Original entry on oeis.org
1, 3, 30, 378, 5382, 82377, 1323153, 21998493, 375346062, 6534966438, 115634273139, 2073448947960, 37593341804520, 688026597386004, 12694000438662381, 235845671565830850, 4408763725976408766, 82861865131590443808, 1564885072909535335695
Offset: 0
-
a(n) = sum(k=0, n, 9^k*binomial(n/3+k-2/3, k)*binomial(k, n-k))/(n+1);
Showing 1-4 of 4 results.