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
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a(n) = (-1)^(n-1)*sum(k=0, n, binomial(2*k-1, k)*binomial(n-2, n-k)/(2*k-1));
A366328
G.f. satisfies A(x) = (1 + x) * (1 + x/A(x)^4).
Original entry on oeis.org
1, 2, -7, 60, -612, 6898, -82806, 1038076, -13431940, 178040315, -2405137161, 32992706368, -458336721104, 6435090557964, -91167680664004, 1301665779507128, -18710805300530504, 270559054510943509, -3932893180646204203, 57437414168562779574, -842365843304975785062
Offset: 0
-
a(n) = (-1)^(n-1)*sum(k=0, n, binomial(5*k-1, k)*binomial(n+3*k-2, n-k)/(5*k-1));
A366358
G.f. satisfies A(x) = 1/(1 - x) + x/A(x)^3.
Original entry on oeis.org
1, 2, -5, 40, -319, 2908, -28151, 284908, -2977115, 31875709, -347884084, 3855802690, -43283239649, 491083601339, -5622489637406, 64877058557080, -753705528179423, 8808460811302729, -103487549564845199, 1221565052783161764, -14480208437556590345
Offset: 0
-
a(n) = (-1)^(n-1)*sum(k=0, n, binomial(4*k-1, k)*binomial(4*k-1, n-k)/(4*k-1));
Showing 1-4 of 4 results.