A071726 Expansion of (1+x^3*C)*C, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.

1, 1, 2, 6, 16, 47, 146, 471, 1562, 5291, 18226, 63648, 224808, 801686, 2882452, 10437745, 38032110, 139339635, 512996370, 1896907980, 7041759120, 26233530210, 98046684060, 367525880670, 1381386710964, 5205006015102

Offset: 0

Author

N. J. A. Sloane, Jun 06 2002

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..1000
• Stoyan Dimitrov, On permutation patterns with constrained gap sizes, arXiv:2002.12322 [math.CO], 2020.

Programs

Mathematica

With[{$MaxExtraPrecision = 1000}, CoefficientList[Series[# (1 + x^3*#) &[(1 - (1 - 4 x)^(1/2))/(2 x)], {x, 0, 25}], x]] (* Michael De Vlieger, May 30 2020 *)