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%I #15 Jul 10 2024 09:37:12
%S 1,7,42,210,966,4158,17094,67782,261261,983983,3635632,13217568,
%T 47393892,167919948,588772152,2045481480,7048466271,24111291897,
%U 81939285582,276810647190,930096277110,3109797881190,10350813392010,34309326304890,113288127469335
%N Expansion of 1/(1 - 2*x - 3*x^2)^(7/2).
%F a(0) = 1, a(1) = 7; a(n) = ((2*n+5)*a(n-1) + 3*(n+5)*a(n-2))/n.
%F a(n) = (binomial(n+6,3)/20) * Sum_{k=0..floor(n/2)} binomial(n+3,n-2*k) * binomial(2*k+3,k).
%F a(n) = Pochhammer(n+1, 6)*hypergeom([(1-n)/2, -n/2], [4], 4)/6!. - _Stefano Spezia_, Jul 10 2024
%t a[n_]:= Pochhammer[n+1, 6]*Hypergeometric2F1[(1-n)/2, -n/2, 4, 4]/6!; Array[a,25,0] (* _Stefano Spezia_, Jul 10 2024 *)
%o (PARI) a(n) = binomial(n+6, 3)/20*sum(k=0, n\2, binomial(n+3, n-2*k)*binomial(2*k+3, k));
%Y Cf. A002426, A102839, A245551.
%K nonn,new
%O 0,2
%A _Seiichi Manyama_, Jul 09 2024
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