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

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..750 (terms 0..100 from Vincenzo Librandi)

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) ).

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}]

Prog

(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);
(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

Crossrefs

Cf. A132276.

Sequence in context: A180038 A052896 A215128 * A025599 A162973 A321989

Adjacent sequences: A190152 A190153 A190154 * A190156 A190157 A190158

Keyword

nonn,easy

Author

Emanuele Munarini, May 05 2011

Status

approved