The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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:=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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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