A191501 Expansion of 2-sqrt(1-4*x-4*x^2-4*x^3)

1, 2, 4, 10, 28, 96, 354, 1372, 5512, 22740, 95768, 410016, 1779210, 7807724, 34589432, 154488460, 694883528, 3144917888, 14311109396, 65439770904, 300534169744, 1385612474536, 6410981989808, 29757955549888, 138534010818650, 646663905140300

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Formula

a(n)=2*sum(k=1..n, (binomial(2*k-2,k-1) * sum(j=0..k, binomial(j,n-3*k+2*j) * binomial(k,j) ) )/k ), n>0, a(0)=1.

D-finite with recurrence: n*a(n) +2*(-2*n+3)*a(n-1) +4*(-n+3)*a(n-2) +2*(-2*n+9)*a(n-3)=0. - R. J. Mathar, Jan 25 2020

Prog

(Maxima)
a(n):=2*sum((binomial(2*k-2, k-1)*sum(binomial(j, n-3*k+2*j)*binomial(k, j), j, 0, k))/k, k, 1, n);

Crossrefs

Sequence in context: A361912 A188496 A369079 * A085549 A022492 A352068

Adjacent sequences: A191498 A191499 A191500 * A191502 A191503 A191504

Keyword

nonn

Author

Vladimir Kruchinin, Jun 03 2011

Status

approved