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a(n) = binomial(n-h,h)*hypergeometric([h-n/2,h-(n-1)/2],[1],4), h = floor(n/4).
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%I #26 Jun 18 2024 02:11:21

%S 1,1,3,7,9,28,95,306,285,1071,3948,14148,11844,47160,182655,690580,

%T 547965,2244385,8961953,35016345,26885859,112052304,456606332,

%U 1824478488,1369818996,5777515212,23884958520,97002706248,71654875560,304865648208,1273989485439

%N a(n) = binomial(n-h,h)*hypergeometric([h-n/2,h-(n-1)/2],[1],4), h = floor(n/4).

%C Also middle column of A132885.

%C a(n) is the k-th term of n-th row of triangle of A132885 where k = floor(n/4). - _Altug Alkan_, Nov 29 2015

%F a(n) = A132885(n, floor(n/4)), that is, a(n) = A132885(A054925(n+2) - 1). - _Altug Alkan_, Nov 29 2015

%p a := proc(n) local h; h := iquo(n,4); binomial(n-h,h)*hypergeom([h-n/2, h-n/2+1/2],[1],4) end: seq(round(evalf(a(n),99)),n=0..30);

%t a[n_] := With[{h = Quotient[n, 4]}, Binomial[n-h, h]*Hypergeometric2F1[h-n/2, h-(n-1)/2, 1, 4]];

%t Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Jun 18 2024 *)

%Y Cf. A132885.

%K nonn

%O 0,3

%A _Peter Luschny_, Sep 18 2014