A366326
G.f. satisfies A(x) = (1 + x) * (1 + x/A(x)^2).
Original entry on oeis.org
1, 2, -3, 14, -78, 479, -3131, 21372, -150588, 1087057, -7998295, 59763129, -452257495, 3459109408, -26697940390, 207672518808, -1626400971710, 12813379464399, -101482102525511, 807524595076284, -6452856224076654, 51760509258982478, -416620859045829372
Offset: 0
-
a(n) = (-1)^(n-1)*sum(k=0, n, binomial(3*k-1, k)*binomial(n+k-2, n-k)/(3*k-1));
A366325
G.f. satisfies A(x) = (1 + x) * (1 + x/A(x)).
Original entry on oeis.org
1, 2, -1, 3, -10, 36, -137, 543, -2219, 9285, -39587, 171369, -751236, 3328218, -14878455, 67030785, -304036170, 1387247580, -6363044315, 29323149825, -135700543190, 630375241380, -2938391049395, 13739779184085, -64430797069375, 302934667061301, -1427763630578197
Offset: 0
-
a := proc(n) option remember; if n = 1 then 2 elif n = 2 then -1 else (-3*(2*n - 3)*a(n-1) - 5*(n - 3)*a(n-2))/n fi; end:
seq(a(n), n = 1..30); # Peter Bala, Sep 10 2024
-
a(n) = (-1)^(n-1)*sum(k=0, n, binomial(2*k-1, k)*binomial(n-2, n-k)/(2*k-1));
A366327
G.f. satisfies A(x) = (1 + x) * (1 + x/A(x)^3).
Original entry on oeis.org
1, 2, -5, 33, -260, 2263, -20979, 203124, -2030121, 20786694, -216928144, 2298911699, -24673591005, 267644087524, -2929602893537, 32317666058508, -358931896710948, 4010200327457883, -45040693394259858, 508253687784232108, -5759468659295939684
Offset: 0
-
a(n) = (-1)^(n-1)*sum(k=0, n, binomial(4*k-1, k)*binomial(n+2*k-2, n-k)/(4*k-1));
A366359
G.f. satisfies A(x) = 1/(1 - x) + x/A(x)^4.
Original entry on oeis.org
1, 2, -7, 69, -715, 8351, -103735, 1346247, -18035023, 247520970, -3462344959, 49181268701, -707502644111, 10286493363184, -150913708053635, 2231345941617611, -33215679733509159, 497392118745778015, -7487512016559918595, 113242852989349372915
Offset: 0
-
a(n) = (-1)^(n-1)*sum(k=0, n, binomial(5*k-1, k)*binomial(5*k-1, n-k)/(5*k-1));
Showing 1-4 of 4 results.