A352150 a(n) = Sum_{k=0..n-1} (-1)^k * binomial(n,k)^2 * (n-k-1)!.

0, 1, -3, 2, -6, -1, -5, 132, 1624, 17145, 174509, 1789842, 18659146, 196678143, 2057524963, 20460314396, 171030108768, 529697015489, -27050118799923, -1079945984126798, -30289996673371254, -765129844741436785, -18575997643525737477, -444653043972658034044

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Formula

Sum_{n>=0} a(n) * x^n / (n!)^2 = BesselJ(0,2*sqrt(x)) * (Ei(x) - log(x) - gamma).

Mathematica

Table[Sum[(-1)^k Binomial[n, k]^2 (n - k - 1)!, {k, 0, n - 1}], {n, 0, 23}]
nmax = 23; Assuming[x > 0, CoefficientList[Series[BesselJ[0, 2 Sqrt[x]] (ExpIntegralEi[x] - Log[x] - EulerGamma), {x, 0, nmax}], x]] Range[0, nmax]!^2

Prog

(PARI) a(n) = sum(k=0, n-1, (-1)^k * binomial(n, k)^2 * (n-k-1)!); \\ Michel Marcus, Mar 06 2022

Crossrefs

Cf. A002741, A009940, A352149.

Sequence in context: A248645 A344323 A368826 * A161826 A097887 A019761

Adjacent sequences: A352147 A352148 A352149 * A352151 A352152 A352153

Keyword

sign

Author

Ilya Gutkovskiy, Mar 06 2022

Status

approved