A362165 Expansion of e.g.f. exp(-x * sqrt(1-2*x)).

1, -1, 3, -4, 25, 24, 721, 5942, 82209, 1186280, 19956241, 373942194, 7768988833, 177018731876, 4389959146665, 117700102748654, 3392361669670081, 104592876707106672, 3434908281762030049, 119702402508549928490, 4411764405039931048641

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

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

D-finite with recurrence a(n) +2*(-n+3)*a(n-1) +2*(-3*n+10)*a(n-2) +6*(n-2)*a(n-3) -9*(n-3)^2*a(n-4) -27*(n-3)*(n-4)*a(n-5)=0. - R. J. Mathar, Dec 04 2023

Maple

A362165 := proc(n)
    (-1)^n*n!*add(2^k * binomial((n-k)/2, k)/(n-k)!, k=0..n) ;
end proc:
seq(A362165(n), n=0..70) ; # R. J. Mathar, Dec 04 2023

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*sqrt(1-2*x))))

Crossrefs

Cf. A115329, A362161, A362163.

Sequence in context: A065809 A093600 A128778 * A338425 A304210 A245244

Adjacent sequences: A362162 A362163 A362164 * A362166 A362167 A362168

Keyword

sign

Author

Seiichi Manyama, Apr 10 2023

Status

approved