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A208508 Triangle of coefficients of polynomials u(n,x) jointly generated with A208509; see the Formula section. 4
1, 1, 1, 1, 4, 1, 9, 1, 1, 16, 6, 1, 25, 20, 1, 1, 36, 50, 8, 1, 49, 105, 35, 1, 1, 64, 196, 112, 10, 1, 81, 336, 294, 54, 1, 1, 100, 540, 672, 210, 12, 1, 121, 825, 1386, 660, 77, 1, 1, 144, 1210, 2640, 1782, 352, 14, 1, 169, 1716, 4719, 4290, 1287, 104, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
col 1: A000012
col 2: A000290 (squares)
col 3: A002415
col 4: A040977
col 5: A054334
row sums, u(n,1): A083329
LINKS
FORMULA
u(n,x)=u(n-1,x)+x*v(n-1,x),
v(n,x)=u(n-1,x)+v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
1...1
1...4
1...9....1
1...16...6
First five polynomials u(n,x):
1
1 + x
1 + 4x
1 + 9x + x^2
1 + 16x + 6x^2
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];
v[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
Table[Expand[u[n, x]], {n, 1, z/2}]
Table[Expand[v[n, x]], {n, 1, z/2}]
cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
TableForm[cu]
Flatten[%] (* A208508 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A208509 *)
CROSSREFS
Cf. A208509.
Sequence in context: A143469 A360610 A331147 * A123726 A323600 A336851
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Feb 27 2012
STATUS
approved

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Last modified February 23 06:36 EST 2024. Contains 370267 sequences. (Running on oeis4.)