A121913
a(n) = 2^(n*(2*n+3)) = 2^A014106(n).
Original entry on oeis.org
1, 32, 16384, 134217728, 17592186044416, 36893488147419103232, 1237940039285380274899124224, 664613997892457936451903530140172288, 5708990770823839524233143877797980545530986496
Offset: 0
Det(1) = 1; Det(1,1; 1,33) = 32; Det(1,1,33; 1,33,97; 33,97,1729) = 16384; ...
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[2^(n*(2*n+3)): n in [0..10]]; // Vincenzo Librandi, Jul 05 2011
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A121913:=n->2^(n*(2*n+3)); seq(A121913(k),k=0..20); # Wesley Ivan Hurt, Oct 24 2013
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Table[2^(n(2n+3)), {n,0,20}] (* Wesley Ivan Hurt, Oct 24 2013 *)
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vector(20, n, n--; 2^(n*(2*n+3))) \\ G. C. Greubel, Oct 08 2018
A385639
a(n) = Sum_{k=0..n} binomial(4*n+1,k) * binomial(2*n-k,n-k).
Original entry on oeis.org
1, 7, 69, 748, 8485, 98847, 1171884, 14066808, 170421669, 2079531685, 25520363869, 314653207128, 3894577133356, 48362609654548, 602248101550920, 7517853111444528, 94044248726758821, 1178641094940246897, 14796230460187072719, 186022053254555479500, 2341837809478393341885
Offset: 0
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Table[Sum[Binomial[4*n+1, k]*Binomial[2*n-k, n-k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Aug 07 2025 *)
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a(n) = sum(k=0, n, binomial(4*n+1, k)*binomial(2*n-k, n-k));
A358114
a(n) = [x^n] (16*x*(32*x - 3) + 1)^(-1/2).
Original entry on oeis.org
1, 24, 608, 16128, 443904, 12570624, 363708416, 10694295552, 318301929472, 9562594738176, 289380790960128, 8807948507676672, 269349580129173504, 8268747111256817664, 254668380196759928832, 7865254221563736096768, 243493498808268962660352, 7553805204299934842486784
Offset: 0
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ogf := (16*x*(32*x - 3) + 1)^(-1/2): ser := series(ogf, x, 20):
seq(coeff(ser, x, n), n = 0..17);
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a[n_] := 16^n * HypergeometricPFQ[{1/2, -n}, {1}, -1]; Array[a, 18, 0] (* Amiram Eldar, Nov 12 2022 *)
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