A115137 Second diagonal of triangle A113647 (called Y(2,1)).

1, 1, 7, 41, 247, 1545, 9975, 66057, 446455, 3067913, 21372919, 150618121, 1071841271, 7691763721, 55600938999, 404488323081, 2959189475319, 21757613309961, 160691417776119, 1191577871450121, 8868160862158839

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Formula

a(n)= b(n) - 2*b(n-1) with b(n):=A062992(n)= A064062(n+1), n>=1. a(0):=1.

G.f.: (1-2*x)*(2*c(2*x)-1)/(1+x) with c(x) g.f. of A000108 (Catalan).

a(n)= A113647(n, n), n>=1.

Recurrence: (n-2)*(n+1)*a(n) = (7*n^2-19*n+14)*a(n-1) + 4*(n-1)*(2*n-3)*a(n-2). - Vaclav Kotesovec, Oct 19 2012

a(n) ~ 2^(3*n+2)/(3*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 19 2012

Example

41=a(3)= A062992(3) - 2*A062992(2) = 67 - 2*13.

Mathematica

CoefficientList[Series[(1-2*x)*(2*(1-Sqrt[1-8*x])/(4*x)-1)/(1+x), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 19 2012 *)

Crossrefs

Sequence in context: A287810 A292035 A108983 * A036730 A258941 A080047

Adjacent sequences: A115134 A115135 A115136 * A115138 A115139 A115140

Keyword

nonn,easy

Author

Wolfdieter Lang, Jan 13 2006

Status

approved