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A210756 Triangle of coefficients of polynomials v(n,x) jointly generated with A210755; see the Formula section. 3
1, 3, 2, 6, 10, 5, 10, 30, 33, 12, 15, 70, 127, 100, 29, 21, 140, 371, 472, 291, 70, 28, 252, 910, 1656, 1624, 822, 169, 36, 420, 1974, 4800, 6640, 5294, 2273, 408, 45, 660, 3906, 12144, 22166, 24702, 16589, 6184, 985, 55, 990, 7194, 27720, 63954 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Column 1: triangular numbers, A000217
Coefficient of v(n,x): A000129(n)
Row sums: A002450
Alternating row sums: 1,1,1,1,1,1,1,1,1,...
For a discussion and guide to related arrays, see A208510.
LINKS
FORMULA
u(n,x)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,
v(n,x)=(x+1)*u(n-1,x)+(x+1)*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
3....2
6....10...5
10...30...33....12
15...70...127...100...29
First three polynomials v(n,x): 1, 3 + 2x, 6 + 10x + 5x^2
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
v[n_, x_] := (x + 1)*u[n - 1, x] + (x + 1)*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[%] (* A210755 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210756 *)
Table[u[n, x] /. x -> 1, {n, 1, z}] (* A002450 *)
Table[v[n, x] /. x -> 1, {n, 1, z}] (* A002450 *)
CROSSREFS
Sequence in context: A245609 A365789 A072765 * A210748 A331889 A369247
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 25 2012
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)