A190253 Central coefficients of the Riordan matrix (g(x),x*g(x)), where g(x) = (1-x-sqrt(1-2x-3x^2-4x^3))/(2*x^2*(1+x)) (A190252).

1, 2, 9, 48, 265, 1512, 8813, 52112, 311427, 1876290, 11376893, 69341868, 424445996, 2607388252, 16066200465, 99256947520, 614611513599, 3813391239444, 23702418040232, 147557273500400, 919907826138042, 5742264749678028, 35886019625941713

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..122 from Vincenzo Librandi)

Formula

a(n) = T(2n,n), where T(n,k) = A190252(n,k).

Mathematica

Table[Sum[Binomial[n+2i, i]((n+1)/(n+i+1))Sum[Binomial[i, j]Binomial[2n-j, n+2i], {j, 0, i}], {i, 0, n/2}], {n, 0, 22}]

Prog

(Maxima) makelist(sum(binomial(n+2*i, i)*(n+1)/(n+i+1)*sum(binomial(i, j)*binomial(2*n-j, n+2*i), j, 0, i), i, 0, n/2), n, 0, 22);
(PARI) a(n)=sum(i=0, n\2, binomial(n+2*i, i)*(n+1)/(n+i+1)*sum(j=0, i, binomial(i, j)*binomial(2*n-j, n+2*i))) \\ Charles R Greathouse IV, Jun 29 2011

Crossrefs

Cf. A190252.

Sequence in context: A188818 A047139 A190315 * A174687 A047059 A153297

Adjacent sequences: A190250 A190251 A190252 * A190254 A190255 A190256

Keyword

nonn

Author

Emanuele Munarini, May 06 2011

Status

approved