A277395 a(n) = Sum_{k=0..n} binomial(n+1,k+1)*A001003(k).

1, 3, 9, 33, 145, 713, 3745, 20513, 115713, 667329, 3916033, 23305857, 140327681, 853262465, 5231925761, 32313686529, 200843829249, 1255308123137, 7884792852481, 49745076576257, 315091155558401, 2003009460686849, 12774610185633793

Offset: 0

Author

Vladimir Kruchinin, Oct 12 2016

Keywords

• nonn

Crossrefs

Cf. A001003.

Programs

Maple

f := gfun:-rectoproc({(n + 1)*a(n) + 2*(-5*n + 1)*a(n - 1) + (25*n - 23)*a(n - 2) + 12*(-2*n + 3)*a(n - 3) + 8*(n - 2)*a(n - 4) = 0, a(0) = 1, a(1) = 3, a(2) = 9, a(3) = 33}, a(n), remember); map(f, [$ (0 .. 20)]); # Georg Fischer, Feb 13 2020

Maxima

g(k):=1/(k+1)*sum((-1)^j*2^(k-j)*binomial(k+1,j)*binomial(2*k-j,k),j,0,k);
makelist(sum(binomial(n+1,k+1)*g(k),k,0,n),n,0,23);

Formula

G.f.: (1-sqrt(8*x^2-8*x+1))/(4*(1-x)^2*x).

D-finite with recurrence: (n+1)*a(n) +2*(-5*n+1)*a(n-1) +(25*n-23)*a(n-2) +12*(-2*n+3)*a(n-3) +8*(n-2)*a(n-4)=0. - R. J. Mathar, Mar 12 2017