A134378 A084938 * [1,2,3,...], where A084938 is taken as lower triangular matrix.

1, 2, 5, 14, 44, 158, 663, 3310, 19759, 139660, 1147120, 10729684, 112309193, 1297522650, 16371057801, 223716758346, 3289199827236, 51745234494858, 867023125576027, 15411557297930534, 289610871340870883, 5736017561257017128, 119413599371241577016

Offset: 0

Author

Gary W. Adamson, Oct 22 2007, corrected Oct 26 2007

Keywords

• nonn

Examples

			a(4) = 44 = (0, 6, 5, 3, 1) dot (1, 2, 3, 4, 5) = (0 + 12 + 15 + 12 + 5).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..170

Crossrefs

Cf. A084938, A260532.

Programs

Maple

series((1-x*hypergeom([1,1],[],x))^(-2), x=0, 50);  # appears to generate the sequence - Mark van Hoeij, Apr 22 2013

Mathematica

CoefficientList[Series[1/(1-x*HypergeometricPFQ[{1, 1}, {}, x])^2, {x, 0, 20}], x] (* Vaclav Kotesovec, Mar 17 2015 after Mark van Hoeij *)
CoefficientList[Assuming[Element[x,Reals], Series[E^(2/x)/(ExpIntegralEi[1/x]-E^(1/x))^2, {x,0,25}]],x] (* Vaclav Kotesovec, Aug 03 2015 *)

Formula

a(n) ~ 2 * (n-1)! * (1 + 3/n + 12/n^2 + 58/n^3 + 327/n^4 + 2107/n^5 + 15329/n^6 + 125041/n^7 + 1139467/n^8 + 11582187/n^9 + 131230827/n^10). - Vaclav Kotesovec, Mar 17 2015

Extensions

More terms from Alois P. Heinz, Apr 27 2012