A144380 Third subdiagonal of A142458: a(n) = A142458(n+3,n).

1, 166, 5482, 109640, 1709675, 23077694, 284433852, 3300384000, 36740695125, 397251942790, 4206505251886, 43874389439176, 452588032465727, 4630933106076350, 47101176806668160, 476947462419456864, 4813761757416769257, 48466731584985480870, 487104579690137249650, 4889039701269534580360

Offset: 1

Author

Roger L. Bagula and Gary W. Adamson, Oct 01 2008

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..990
• Index entries for linear recurrences with constant coefficients, signature (40,-675,6294,-35679,127548,-289173,409062,-347112,161056,-31360).

Crossrefs

Cf. A142458, A142976.

Programs

Magma

[(1/162)*( 8*10^(n+3) - 30*(3*n +8)*7^(n+2) + 6*(9*n^2 +39*n +40)*4^(n+2) - (27*n^3 +135*n^2 +198*n +80)): n in [1..30]]; // G. C. Greubel, Mar 15 2022

Mathematica

T[n_, k_, m_]:= T[n, k, m]= If[k==1 || k==n, 1, (m*n-m*k+1)*T[n-1,k-1,m] + (m*k - m+1)*T[n-1,k,m]];
A144380[n_]:= T[n+3, n, 3];
Table[A144380[n], {n,30}] (* modified by G. C. Greubel, Mar 15 2022 *)

Sage

@CachedFunction
def T(n,k,m):
    if (k==1 or k==n): return 1
    else: return (m*(n-k)+1)*T(n-1,k-1,m) + (m*k-m+1)*T(n-1,k,m)
def A144380(n): return T(n+3, n, 3)
[A144380(n) for n in (1..30)] # G. C. Greubel, Mar 15 2022

Formula

G.f.: x*(1 +126*x -483*x^2 -3884*x^3 +15300*x^4 -10848*x^5 -8960*x^6)/ ( (1-10*x) *(1-7*x)^2 *(1-4*x)^3 *(1-x)^4 ). - R. J. Mathar, Sep 14 2013

a(n) = (1/162)*( 8*10^(n+3) - 30*(3*n +8)*7^(n+2) + 6*(9*n^2 +39*n +40)*4^(n+2) - (27*n^3 +135*n^2 +198*n +80)). - G. C. Greubel, Mar 15 2022