A145138 Main diagonal of square array A145153.

0, 1, 2, 6, 20, 71, 259, 960, 3597, 13586, 51635, 197223, 756380, 2910707, 11233311, 43460144, 168502849, 654547456, 2546819347, 9924285801, 38723794820, 151278566731, 591628491483, 2316065644414, 9074988880769, 35587925333525, 139666503235814, 548516611541343

Offset: 0

Author

Alois P. Heinz, Oct 03 2008

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A145153, A000004, A000012, A001477, A000217, A000292, A145126, A145127, A145128, A145129, A145130, A017898, A003269, A098578, A145131, A145132, A145133, A145134, A145135, A145136, A145137.

Programs

Maple

a:= n-> coeftayl(x/(1-x-x^4)/(1-x)^(n-1), x=0, n):
seq(a(n), n=0..30);
# second Maple program:
a:= proc(n) option remember; `if`(n<5, n*(n+1)*(n^2-4*n+6)/6,
       a(n-4)+(2*(35*n^3-207*n^2+310*n-78)*a(n-1)-(203*n^3
       -1244*n^2+1891*n-130)*a(n-2)+(2*n-7)*(7*n-19)*n*
       (10*a(n-3)-2*a(n-5)))/((7*n-26)*(n-1)^2))
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Aug 18 2019

Mathematica

a[n_] := SeriesCoefficient[x/(1-x-x^4)/(1-x)^(n-1), {x, 0, n}];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, May 10 2022 *)

Formula

a(n) = [x^n] x/((1-x-x^4)*(1-x)^(n-1)).