A369724 Expansion of e.g.f. exp( (5/2) * (1-sqrt(1-4*x)) ).

1, 5, 35, 335, 4225, 67525, 1321075, 30751775, 832573025, 25745985125, 896177819875, 34698406783375, 1479737530398625, 68935386567921125, 3483762766656021875, 189846574063623209375, 11098195364856546690625, 692834276972696475053125

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

a(0) = 1; a(n) = Sum_{k=0..n-1} 5^(n-k) * (n-1+k)! / (k! * (n-1-k)!).

a(n) = 2*(2*n-3)*a(n-1) + 25*a(n-2).

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(5/2*(1-sqrt(1-4*x)))))

Crossrefs

Cf. A001517, A101682, A243953, A369722, A369723.

Cf. A000108.

Sequence in context: A113342 A262248 A346666 * A360611 A201367 A233860

Adjacent sequences: A369721 A369722 A369723 * A369725 A369726 A369727

Keyword

nonn

Author

Seiichi Manyama, Jan 30 2024

Status

approved