The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A155950 A triangle of polynomial coefficients: q(x,n)=(1 - x)^(n + 1)*Sum[(2*k + n)^n*x^k, {k, 0, Infinity}]; p(x,n)=q(x,n)+x^n*q(1/x,n). 0
 1, 1, 2, 2, 8, 8, 26, 22, 22, 26, 272, -64, 352, -64, 272, 2882, -486, 1444, 1444, -486, 2882, 50752, -93056, 230336, -283904, 230336, -93056, 50752, 745418, -1182562, 2112618, -1030354, -1030354, 2112618, -1182562, 745418, 18456832, -66045952 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Row sums are: {2, 4, 16, 96, 768, 7680, 92160, 1290240, 20643840, 371589120, 7431782400,...}. LINKS FORMULA q(x,n)=(1 - x)^(n + 1)*Sum[(2*k + n)^n*x^k, {k, 0, Infinity}]; p(x,n)=q(x,n)+x^n*q(1/x,n); t(n,m)=coefficients(p(x,n)) EXAMPLE {1, 1}, {2, 2}, {8, 8}, {26, 22, 22, 26}, {272, -64, 352, -64, 272}, {2882, -486, 1444, 1444, -486, 2882}, {50752, -93056, 230336, -283904, 230336, -93056, 50752}, {745418, -1182562, 2112618, -1030354, -1030354, 2112618, -1182562, 745418}, {18456832, -66045952, 193838080, -342063104, 412272128, -342063104, 193838080, -66045952, 18456832}, {347066882, -1114674254, 2662543720, -3229707896, 1520566108, 1520566108, -3229707896, 2662543720, -1114674254, 347066882}, {11073741824, -59833329664, 216555369472, -500687839232, 812895791104, -952575684608, 812895791104, -500687839232, 216555369472, -59833329664, 11073741824} MATHEMATICA Clear[p, x, n, m]; p[x_, n_] = (1 - x)^(n + 1)*Sum[(2*k + n)^n*x^k, {k, 0, Infinity}]; Table[FullSimplify[ExpandAll[p[x, n]]], {n, 0, 10}]; Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x] + Reverse[ CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x]], {n, 0, 10}]; Flatten[%] CROSSREFS Sequence in context: A099328 A073090 A120544 * A162959 A158302 A007083 Adjacent sequences:  A155947 A155948 A155949 * A155951 A155952 A155953 KEYWORD sign,tabl,uned AUTHOR Roger L. Bagula, Jan 31 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 January 17 22:33 EST 2022. Contains 350410 sequences. (Running on oeis4.)