This site is supported by donations to The OEIS Foundation.

 Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A248669 Triangular array of coefficients of polynomials q(n,k) defined in Comments. 9
 1, 2, 1, 5, 4, 1, 16, 17, 7, 1, 65, 84, 45, 11, 1, 326, 485, 309, 100, 16, 1, 1957, 3236, 2339, 909, 196, 22, 1, 13700, 24609, 19609, 8702, 2281, 350, 29, 1, 109601, 210572, 181481, 89225, 26950, 5081, 582, 37, 1, 986410, 2004749, 1843901, 984506, 331775 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS q(n,x) = 1 + k+x + (k+x)(k-1+x) + (k+x)(k-1+x)(k-2+x) + ... + (k+x)(k-1+x)(k-2+x)...(1+x).  The arrays at A248229 and A248664 have the same first column, given by A000522(n) for n >= 0.  The alternating row sums of the array at A248669 are also given by A000522; viz., q(n,-1) = q(n-1,0) = A000522(n-2) for n >= 2.  Column 2 of A248669 is given by A093344(n) for n >= 1. LINKS Clark Kimberling, Table of n, a(n) for n = 1..5000 FORMULA q(n,x) = (x + n - 1)*q(n-1,x) + 1, with q(1,x) = 1. EXAMPLE The first six polynomials: p(1,x) = 1 p(2,x) = 2 + x p(3,x) = 5 + 4 x + x^2 p(4,x) = 16 + 17 x + 7 x^2 + x^3 p(5,x) = 65 + 8 x + 45 x^2 + 11 x^3 + x^4 p(6,x) = 326 + 485 x + 309 x^2 + 100 x^3 + 16 x^4 + x^5 First six rows of the triangle: 1 2     1 5     4     1 16    17    7    1 65    84    45   11    1 326   485  309   100   16   1 MATHEMATICA t[x_, n_, k_] := t[x, n, k] = Product[x + n - i, {i, 1, k}]; q[x_, n_] := Sum[t[x, n, k], {k, 0, n - 1}]; TableForm[Table[q[x, n], {n, 1, 6}]]; TableForm[Table[Factor[q[x, n]], {n, 1, 6}]]; c[n_] := c[n] = CoefficientList[q[x, n], x]; TableForm[Table[c[n], {n, 1, 12}]] (* A248669 array *) Flatten[Table[c[n], {n, 1, 12}]]   (* A248669 sequence *) CROSSREFS Cf. A248665, A248666, A248667, A248668, A248670. Sequence in context: A171515 A110271 A073107 * A103718 A113350 A227372 Adjacent sequences:  A248666 A248667 A248668 * A248670 A248671 A248672 KEYWORD nonn,tabl,easy AUTHOR Clark Kimberling, Oct 11 2014 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 December 12 05:15 EST 2018. Contains 318052 sequences. (Running on oeis4.)