A366267
G.f. A(x) satisfies A(x) = 1 + x + x*A(x)^4.
Original entry on oeis.org
1, 2, 8, 56, 448, 3920, 36288, 349440, 3464448, 35125760, 362522624, 3795914240, 40224968704, 430579701760, 4648899846144, 50568103690240, 553632271155200, 6096025799852032, 67464070696927232, 750003531943903232, 8371814935842258944
Offset: 0
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nmax = 20; A[_] = 1;
Do[A[x_] = 1 + x + x*A[x]^4 + O[x]^(nmax+1) // Normal, {nmax+1}];
CoefficientList[A[x], x] (* Jean-François Alcover, Mar 03 2024 *)
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a(n) = sum(k=0, n, binomial(3*k+1, n-k)*binomial(4*k, k)/(3*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
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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
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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));
A366436
G.f. A(x) satisfies A(x) = 1 + x * ((1 - x) / A(x))^3.
Original entry on oeis.org
1, 1, -6, 36, -272, 2304, -20880, 198080, -1942080, 19521792, -200101376, 2083538688, -21976624128, 234321952768, -2521446660096, 27347192389632, -298643542716416, 3280990949720064, -36238161907974144, 402146115064233984, -4481721683926056960
Offset: 0
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a(n) = (-1)^(n-1)*sum(k=0, n, binomial(4*k-1, k)*binomial(3*k, n-k)/(4*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));
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 1-6 of 6 results.