A190155 Central coefficients of the Riordan matrix (g(x),x*g(x)), where g(x) = (1-x-x^2-sqrt(1-2*x-5*x^2+2*x^3+x^4))/(2*x^2) (A132276).
1, 2, 12, 64, 385, 2346, 14672, 92936, 595179, 3841970, 24959726, 162988464, 1068860884, 7034520304, 46437268905, 307351081056, 2038878634695, 13552394472612, 90242046694715, 601847594327000, 4019556724362165, 26879647264387170
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..750 (terms 0..100 from Vincenzo Librandi)
Crossrefs
Cf. A132276.
Programs
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Mathematica
Table[Sum[Binomial[n+2i,i](n+1)/(i+n+1)Sum[Binomial[2n-j,n+2i]Binomial[n-2i-j,j],{j,0,n-2i}],{i,0,n/2}],{n,0,21}] -
Maxima
makelist(sum(binomial(n+2*i,i)*(n+1)/(i+n+1)*sum(binomial(2*n-j,n+2*i)*binomial(n-2*i-j,j),j,0,n-2*i),i,0,n/2),n,0,21);
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PARI
for(n=0,30, print1(sum(i=0,n/2, binomial(n+2*i,i)*((n+1)/(i+n+1)) *sum(j=0, n-2*i, binomial(2*n-j,n+2*i)*binomial(n-2*i-j,j))), ", ")) \\ G. C. Greubel, Dec 28 2017
Formula
a(n) = T(2*n,n) where T(n,k) = A132276(n,k).
a(n) = Sum_{i=0..(n/2)} ( binomial(n+2*i,i)*((n+1)/(i+n+1)) * Sum_{j=0..(n-2*i)} binomial(2*n-j,n+2*i)*binomial(n-2*i-j,j) ).