A292897 a(n) = -Sum_{k=1..3}(-1)^(n-k)*hypergeom([k, k-n-3], [], 1).

3, 7, 27, 129, 755, 5187, 40923, 364333, 3611811, 39448095, 470573723, 6086754297, 84847445907, 1267953887899, 20220829211355, 342759892460517, 6153802869270083, 116652857267320503, 2328215691932062491, 48800672765792988145, 1071780020853500289843

Offset: 0

Author

Peter Luschny, Oct 05 2017

Keywords

• nonn

Crossrefs

Cf. A000166 (m=1), A259834 (m=2), this sequence (m=3), A292898 (m>=1).

Programs

Maple

A292897 := n -> -add((-1)^(n-k)*hypergeom([k, k-n-3], [], 1), k=1..3):
seq(simplify(A292897(n)), n=0..20);

Mathematica

Table[-Sum[(-1)^(n-k)*HypergeometricPFQ[{k, k-n-3}, {}, 1], {k,1,3}], {n,0,20}] (* Vaclav Kotesovec, Jul 05 2018 *)

Formula

a(n) = A292898(3, n).

From Vaclav Kotesovec, Jul 05 2018: (Start)

Recurrence: (5*n^2 - 6*n + 4)*a(n) = (5*n^3 - n^2 - 6*n + 9)*a(n-1) + (n-1)*(5*n^2 + 4*n + 3)*a(n-2).

a(n) ~ 5*sqrt(Pi/2) * n^(n + 5/2) / exp(n+1). (End)