

A117724


Triangle with the coefficient [x^n] x/(1m*x^2x^3) in row n, columns m = 1..n+2.


2



0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 2, 3, 4, 5, 1, 1, 1, 1, 1, 1, 1, 4, 9, 16, 25, 36, 49, 2, 4, 6, 8, 10, 12, 14, 16, 2, 9, 28, 65, 126, 217, 344, 513, 730, 3, 12, 27, 48, 75, 108, 147, 192, 243, 300, 4, 22, 90, 268, 640, 1314, 2422, 4120, 6588, 10030, 14674, 5, 33
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,12


COMMENTS

The column m=1 is A000931. m=2 is essentially A008346, m=3 essentially A052931.
Row n=1 contains a single 0 by convention.


LINKS

Nathaniel Johnston, Table of n, a(n) for n = 1..5000


EXAMPLE

The table starts:
0;
0, 0;
1, 1, 1;
0, 0, 0, 0;
1, 2, 3, 4, 5;
1, 1, 1, 1, 1, 1;
1, 4, 9, 16, 25, 36, 49;
2, 4, 6, 8, 10, 12, 14, 16;
2, 9, 28, 65, 126, 217, 344, 513, 730;
3, 12, 27, 48, 75, 108, 147, 192, 243, 300;


MAPLE

t:=taylor(x/(1m*x^2x^3), x, 11):seq(seq(coeff(t, x, n), m=1..n+2), n=1..10); # Nathaniel Johnston, Apr 27 2011


MATHEMATICA

(* define the polynomial *) p[x_] = x/(1  m*x^2  x^3); (* Taylor derivative expansion of the polynomial*) a = Table[Flatten[{{p[0]}, Table[Coefficient[Series[p[x], {x, 0, 30}], x^n], {n, 1, 10}]}], {m, 1, 10}] (*antidiagonal expansion to give triangular function*) b = Join[{{0}}, Delete[Table[Table[a[[ n]][[m]], {n, 1, m + 1}], {m, 0, 9}], 1]]


CROSSREFS

Cf. A000931.
Sequence in context: A256306 A030548 A346690 * A255826 A339256 A277544
Adjacent sequences: A117721 A117722 A117723 * A117725 A117726 A117727


KEYWORD

nonn,tabl,easy


AUTHOR

Roger L. Bagula, Apr 13 2006


EXTENSIONS

Sign in definition corrected, offset set to 1 by Assoc. Eds. of the OEIS, Jun 15 2010


STATUS

approved



