A188482 Diagonal sums of the Riordan matrix (1/(1-4x),(1-sqrt(1-4x))/(2*sqrt(1-4x))) (A188481).

1, 4, 17, 71, 295, 1221, 5040, 20761, 85380, 350659, 1438568, 5896098, 24145941, 98812861, 404118745, 1651811920, 6748282361, 27556753703, 112482005583, 458958881572, 1872034052651, 7633342954234, 31116252892098, 126806214027741, 516633711969649

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Formula

a(n) = [x^n] 1/((1-x)^(n+1)*(1-2*x-x^2+x^3)).

a(n) = Sum_{k=0..n} Sum_{i=0..k} binomial(k,i)*binomial(2*n+k-2*i+2, n-k)*(-1)^i.

G.f.: (2 - 7*x - 4*x^2 + x*sqrt(1-4*x))/(2 - 14*x + 16*x^2 + 30*x^3 + 8*x^4).

Conjecture: (-n+1)*a(n) + (7*n-9)*a(n-1) + 2*(-4*n+7)*a(n-2) + (-15*n+23)*a(n-3) + 2*(-2*n+3)*a(n-4) = 0. - R. J. Mathar, Jun 14 2016

Mathematica

Table[Sum[Binomial[k, i]Binomial[2n+k-2i+2, n-k](-1)^i, {k, 0, n}, {i, 0, k}], {n, 0, 12}]

Prog

(Maxima) makelist(sum(sum(binomial(k, i)*binomial(2*n+k-2*i+2, n-k)*(-1)^i, i, 0, k), k, 0, n), n, 0, 12);

Crossrefs

Cf. A141223, A188481.

Sequence in context: A017955 A017956 A136792 * A364705 A179606 A108929

Adjacent sequences: A188479 A188480 A188481 * A188483 A188484 A188485

Keyword

nonn,easy

Author

Emanuele Munarini, Apr 01 2011

Status

approved