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

0,3

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.

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 *)

Crossrefs

Sequence in context: A003291 A148442 A190729 * A148443 A148444 A064190

Adjacent sequences: A071723 A071724 A071725 * A071727 A071728 A071729

Keyword

nonn

Author

N. J. A. Sloane, Jun 06 2002

Status

approved