A366268
G.f. A(x) satisfies A(x) = 1 + x + x*A(x)^5.
Original entry on oeis.org
1, 2, 10, 90, 930, 10530, 126282, 1576410, 20268930, 266591490, 3569991370, 48509238810, 667157894050, 9269347395490, 129908752970890, 1834347364277530, 26071297610067970, 372683901080814850, 5354668071305293450, 77286026066830771930
Offset: 0
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a(n) = sum(k=0, n, binomial(4*k+1, n-k)*binomial(5*k, k)/(4*k+1));
A366363
G.f. satisfies A(x) = (1 + x/A(x))/(1 - x).
Original entry on oeis.org
1, 2, 0, 4, -8, 32, -112, 432, -1696, 6848, -28160, 117632, -497664, 2128128, -9183488, 39940864, -174897664, 770452480, -3411959808, 15181264896, -67833868288, 304256253952, -1369404661760, 6182858317824, -27995941060608, 127100310290432, -578433619525632
Offset: 0
-
A366363[n_]:=(-1)^(n-1)Sum[Binomial[2k-1,k]Binomial[k-1,n-k]/(2k-1),{k,0,n}];
Array[A366363,30,0] (* Paolo Xausa, Oct 20 2023 *)
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a(n) = (-1)^(n-1)*sum(k=0, n, binomial(2*k-1, k)*binomial(k-1, n-k)/(2*k-1));
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
-
a(n) = (-1)^(n-1)*sum(k=0, n, binomial(3*k-1, k)*binomial(2*k-1, n-k)/(3*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
-
a(n) = (-1)^(n-1)*sum(k=0, n, binomial(4*k-1, k)*binomial(3*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 1-5 of 5 results.