A118352 Semi-diagonal (one row below central terms) of pendular triangle A118350 and equal to the self-convolution of the central terms (A118351).

1, 2, 13, 96, 770, 6530, 57612, 523446, 4864795, 46032288, 441981816, 4295393886, 42172388820, 417668676206, 4167719552099, 41861139949200, 422890327921650, 4294027462637528, 43801007565527184, 448625344231794792

Offset: 0

Author

Paul D. Hanna, Apr 26 2006

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A118350, A118351, A118353, A118354.

Programs

Mathematica

T[n_, k_]:= T[n, k]= If[k==0, 1, If[k==n, 0, T[n-1, k] -3*T[n-1, k-1] +3*T[n, k-1] +T[n+1, k-1] ]];
Table[T[n, n-2], {n,2,30}] (* G. C. Greubel, Feb 18 2021 *)

PARI

{a(n)=polcoeff((serreverse(x*(1-3*x+sqrt((1-3*x)*(1-7*x)+x*O(x^n)))/2/(1-3*x))/x)^2,n)}

Sage

@CachedFunction
def T(n, k):
    if (k<0 or nG. C. Greubel, Feb 18 2021