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A173048 Triangle T(n, k) = [x^k](p(x, n, q)) where p(x,n,q) = Product_{j=1..n} (x + q^j) + Product_{j=1..n} (x*q^j + 1), p(x, 0, q) = 1, and q = 2, read by rows. 3
1, 3, 3, 9, 12, 9, 65, 70, 70, 65, 1025, 990, 560, 990, 1025, 32769, 31806, 11160, 11160, 31806, 32769, 2097153, 2064510, 671832, 178560, 671832, 2064510, 2097153, 268435457, 266338558, 87413592, 12850368, 12850368, 87413592, 266338558, 268435457 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Rows n = 0..25 of the triangle, flattened

FORMULA

T(n, k) = [x^k](p(x, n, q)) where p(x,n,q) = Product_{j=1..n} (x + q^j) + Product_{j=1..n} (x*q^j + 1), p(x, 0, q) = 1, and q = 2.

EXAMPLE

Triangle begins as:

        1;

        3,       3;

        9,      12,      9;

       65,      70,     70,     65;

     1025,     990,    560,    990,   1025;

    32769,   31806,  11160,  11160,  31806,   32769;

  2097153, 2064510, 671832, 178560, 671832, 2064510, 2097153;

MATHEMATICA

p[x_, n_, q_]:= If[n==0, 1, Product[x+q^j, {j, n}] + Product[x*q^j +1, {j, n}]];

T[n_, k_, q_]:= SeriesCoefficient[p[x, n, q], {x, 0, k}];

Table[T[n, k, 2], {n, 0, 10}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Apr 26 2021 *)

PROG

(Magma)

R<x>:=PowerSeriesRing(Integers(), 50);

p:= func< x, n, q | n eq 0 select 1 else (&*[x+q^j: j in [1..n]]) + (&*[1+q^j*x: j in [1..n]]) >;

T:= func< n, q | Coefficients(R!( p(x, n, q) )) >;

[T(n, 2): n in [0..10]]; // G. C. Greubel, Apr 26 2021

CROSSREFS

Cf. A134058 (q=1), this sequence (q=2), A173049 (q=3).

Sequence in context: A320293 A146153 A339028 * A165992 A117153 A045810

Adjacent sequences:  A173045 A173046 A173047 * A173049 A173050 A173051

KEYWORD

nonn,tabl,easy,less

AUTHOR

Roger L. Bagula, Feb 08 2010

EXTENSIONS

Edited by G. C. Greubel, Apr 26 2021

STATUS

approved

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Last modified May 13 00:11 EDT 2021. Contains 343829 sequences. (Running on oeis4.)