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

0,2

Links

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

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 *)

Prog

(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 n<k): return 0
    elif (k==0): return 1
    elif (k==n): return 0
    else: return T(n-1, k) - 3*T(n-1, k-1) + 3*T(n, k-1) + T(n+1, k-1)
[T(n, n-2) for n in (2..30)] # G. C. Greubel, Feb 18 2021

Crossrefs

Cf. A118350, A118351, A118353, A118354.

Sequence in context: A282724 A104255 A369202 * A320360 A074614 A184019

Adjacent sequences: A118349 A118350 A118351 * A118353 A118354 A118355

Keyword

nonn

Author

Paul D. Hanna, Apr 26 2006

Status

approved