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
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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));
A366366
G.f. satisfies A(x) = (1 + x/A(x)^4)/(1 - x).
Original entry on oeis.org
1, 2, -6, 58, -574, 6402, -75878, 939290, -12000318, 157050178, -2094657926, 28368411194, -389079656446, 5393118559938, -75431624084838, 1063251390845338, -15088643098754942, 215396586102923138, -3091050571516120582, 44566089825496186170
Offset: 0
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a(n) = (-1)^(n-1)*sum(k=0, n, binomial(5*k-1, k)*binomial(4*k-1, n-k)/(5*k-1));
A366357
G.f. satisfies A(x) = 1/(1 - x) + x/A(x)^2.
Original entry on oeis.org
1, 2, -3, 19, -105, 690, -4781, 34708, -260189, 1999169, -15660175, 124596499, -1004110947, 8179379808, -67239070867, 557098881920, -4647368670949, 39001655222788, -329048378867467, 2789241880512899, -23743798316713367, 202894843070927860
Offset: 0
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a(n) = (-1)^(n-1)*sum(k=0, n, binomial(3*k-1, k)*binomial(3*k-1, n-k)/(3*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
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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.