A365759
G.f. satisfies A(x) = 1 + x*A(x)*(1 + x^3*A(x)^5).
Original entry on oeis.org
1, 1, 1, 1, 2, 8, 29, 85, 217, 541, 1471, 4447, 13975, 43103, 129083, 382535, 1147956, 3519462, 10947483, 34162483, 106341406, 330590764, 1030528133, 3229411337, 10170424724, 32127163822, 101633409379, 321862281571, 1020889305476, 3244779281894, 10335256815761
Offset: 0
-
a(n) = sum(k=0, n\4, binomial(n-3*k, k)*binomial(n+2*k+1, n-3*k)/(n+2*k+1));
A365761
G.f. satisfies A(x) = 1 + x*A(x)*(1 + x^2*A(x)^5).
Original entry on oeis.org
1, 1, 1, 2, 8, 29, 91, 289, 1009, 3706, 13606, 49822, 184726, 696052, 2648746, 10132072, 38952970, 150635860, 585724594, 2287631614, 8968247626, 35281363830, 139256375922, 551306272137, 2188516471579, 8709331962133, 34739262293455, 138863195368540
Offset: 0
-
a(n) = sum(k=0, n\3, binomial(n-2*k, k)*binomial(n+3*k+1, n-2*k)/(n+3*k+1));
A365758
G.f. satisfies A(x) = 1 + x*A(x) / (1 - x^4*A(x)^5).
Original entry on oeis.org
1, 1, 1, 1, 1, 2, 8, 29, 85, 212, 481, 1081, 2627, 7100, 20328, 58023, 160430, 430391, 1140892, 3051678, 8334638, 23199896, 65148939, 182781853, 510225082, 1419091293, 3948954920, 11034704856, 31001204632, 87466532564, 247303929326, 699572256145
Offset: 0
-
a(n) = sum(k=0, n\4, binomial(n-3*k-1, k)*binomial(n+k+1, n-4*k)/(n+k+1));
A366025
Expansion of (1/x) * Series_Reversion( x*(1-x)/(1+x^5) ).
Original entry on oeis.org
1, 1, 2, 5, 14, 43, 139, 465, 1595, 5577, 19804, 71228, 258946, 950030, 3513050, 13079920, 48993149, 184490361, 698020080, 2652192675, 10115878915, 38717526745, 148655862210, 572412768275, 2209969761924, 8553073927858, 33176952295730, 128960722306128
Offset: 0
-
CoefficientList[InverseSeries[Series[x(1-x)/(1+x^5),{x,0,28}],x]/x,x] (* Stefano Spezia, Sep 26 2023 *)
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a(n) = sum(k=0, n\5, binomial(n-4*k, k)*binomial(2*n-5*k+1, n-4*k)/(2*n-5*k+1));
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Vec(serreverse(x*(1-x)/(1+x^5)+O(x^30))/x) \\ Michel Marcus, Sep 26 2023
Showing 1-4 of 4 results.