A090439 Alternating row sums of array A090438 ((4,2)-Stirling2).

1, 5, 37, -887, -168919, -21607859, -2799384755, -337767590383, -11912361112367, 21032925955607701, 16703816669710968821, 10654267957172226744985, 6614425802684094455696377, 4120103872599589439389105373

Offset: 1

Author

Wolfdieter Lang, Dec 23 2003

Keywords

• sign
• easy

Programs

Maple

# assuming offset 0:
p := (n,x) -> (2*n+2)!*hypergeom([-2*n],[3],x)/2;
seq(simplify(p(n,1)), n=0..11); # Peter Luschny, Apr 08 2015

Mathematica

a[n_, k_] := (-1)^k/k! Sum[(-1)^p Binomial[k, p] Product[FactorialPower[p + 2(j-1), 2], {j, 1, n}], {p, 2, k}];
a[n_] := Sum[(-1)^k a[n,k], {k, 2, 2n}];
Array[a,14] (* Jean-François Alcover, Jun 05 2019 *)

Formula

a(n) = Sum_{k=2..2*n} ((-1)^k)*A090438(n, k), n>=1, a(0):= 1.

a(n) = (2*n+2)!*hypergeom([-2*n],[3],1)/2, assuming offset 0. - Peter Luschny, Apr 08 2015