A366364
G.f. satisfies A(x) = (1 + x/A(x)^2)/(1 - x).
Original entry on oeis.org
1, 2, -2, 14, -70, 426, -2714, 18118, -124814, 881042, -6339058, 46318334, -342769750, 2563781690, -19350683018, 147197511222, -1127334112542, 8685458120226, -67270210217186, 523472089991662, -4090668558473318, 32088204418069450, -252576222775705466
Offset: 0
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a(n) = (-1)^(n-1)*sum(k=0, n, binomial(3*k-1, k)*binomial(2*k-1, n-k)/(3*k-1));
A366356
G.f. satisfies A(x) = 1/(1 - x) + x/A(x).
Original entry on oeis.org
1, 2, -1, 6, -17, 71, -292, 1284, -5807, 26961, -127627, 613815, -2990680, 14730714, -73229290, 366936232, -1851352819, 9397497759, -47957377933, 245903408245, -1266266092111, 6545667052321, -33954266444497, 176689391245147, -922112642288148, 4825154135801698
Offset: 0
-
A366356[n_]:=(-1)^(n-1)Sum[Binomial[2k-1,k]Binomial[2k-1,n-k]/(2k-1),{k,0,n}];
Array[A366356,30,0] (* Paolo Xausa, Oct 20 2023 *)
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a(n) = (-1)^(n-1)*sum(k=0, n, binomial(2*k-1, k)*binomial(2*k-1, n-k)/(2*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));
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.