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!)
 A159040 A triangle of polynomial coefficients: p(x,n)=Sum[x^i*If[i == Floor[n/2] && Mod[n, 2] == 0, 0, If[i <= (less than or equal) Floor[n/2], (-1)^i*A109128[n, i], -(-1)^(n - i)* A109128[n, i]]], {i, 0, n}]/(1 - x). 0
 1, 1, 1, 1, -4, 1, 1, -6, -6, 1, 1, -8, 11, -8, 1, 1, -10, 19, 19, -10, 1, 1, -12, 29, -40, 29, -12, 1, 1, -14, 41, -70, -70, 41, -14, 1, 1, -16, 55, -112, 139, -112, 55, -16, 1, 1, -18, 71, -168, 251, 251, -168, 71, -18, 1, 1, -20, 89, -240, 419, -504, 419, -240, 89, -20, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are: {1, 2, -2, -10, -3, 20, -4, -84, -5, 274, -6,...}. LINKS FORMULA p(x,n)=Sum[x^i*If[i == Floor[n/2] && Mod[n, 2] == 0, 0, If[i <= (less than or equal) Floor[n/2], (-1)^i*A109128[n, i], -(-1)^(n - i)* A109128[n, i]]], {i, 0, n}]/(1 - x); t(n,m)=coefficients(p(x,n),x) EXAMPLE {1}, {1, 1}, {1, -4, 1}, {1, -6, -6, 1}, {1, -8, 11, -8, 1}, {1, -10, 19, 19, -10, 1}, {1, -12, 29, -40, 29, -12, 1}, {1, -14, 41, -70, -70, 41, -14, 1}, {1, -16, 55, -112, 139, -112, 55, -16, 1}, {1, -18, 71, -168, 251, 251, -168, 71, -18, 1}, {1, -20, 89, -240, 419, -504, 419, -240, 89, -20, 1} MATHEMATICA Clear[A, p, n, i]; A[n_, 0] := 1; A[n_, n_] := 1; A[n_, k_] := A[n - 1, k - 1] + A[n - 1, k] + 1; p[x_, n_] = Sum[x^i*If[i == Floor[n/2] && Mod[n, 2] == 0, 0, If[i <= Floor[n/2], (-1)^i*A[n, i], -(-1)^(n - i)*A[n, i]]], {i, 0, n}]/(1 - x); Table[CoefficientList[FullSimplify[p[x, n]], x], {n, 1, 11}]; Flatten[%] CROSSREFS Sequence in context: A084061 A140262 A049702 * A132046 A141540 A143188 Adjacent sequences:  A159037 A159038 A159039 * A159041 A159042 A159043 KEYWORD sign,tabl,uned AUTHOR Roger L. Bagula, Apr 03 2009 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 February 26 21:29 EST 2020. Contains 332295 sequences. (Running on oeis4.)