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));
A366365
G.f. satisfies A(x) = (1 + x/A(x)^3)/(1 - x).
Original entry on oeis.org
1, 2, -4, 32, -240, 2064, -18816, 179264, -1762816, 17758976, -182342400, 1901196288, -20075427840, 214246524928, -2307200135168, 25039992254464, -273603550461952, 3007387399258112, -33230774508716032, 368915340555517952, -4112806343370539008
Offset: 0
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a(n) = (-1)^(n-1)*sum(k=0, n, binomial(4*k-1, k)*binomial(3*k-1, n-k)/(4*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));
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
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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.