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!)
 A158781 A doubled power MacMahon A060187 infinite sum polynomial from the Eulerian numbers sum by skipping powers: p(x,n)=((1 - x)^ (n + 1))*((1 + x)^ (n + 1))*Sum[(k + 1)^n*x^k, {k, 0, Infinity, 2}] 0
 1, 1, 0, 1, 1, 0, 6, 0, 1, 1, 0, 23, 0, 23, 0, 1, 1, 0, 76, 0, 230, 0, 76, 0, 1, 1, 0, 237, 0, 1682, 0, 1682, 0, 237, 0, 1, 1, 0, 722, 0, 10543, 0, 23548, 0, 10543, 0, 722, 0, 1, 1, 0, 2179, 0, 60657, 0, 259723, 0, 259723, 0, 60657, 0, 2179, 0, 1, 1, 0, 6552, 0, 331612, 0, 2485288 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS Row sums are:A000165;2^n*n!; {1, 2, 8, 48, 384, 3840, 46080, 645120, 10321920, 185794560, 3715891200,..}. p(Sqrt[x],n) gives the MacMahon triangle sequence: A060187. This power skipping approach to infinite sums is a new way to look at them. LINKS FORMULA p(x,n)=((1 - x)^ (n + 1))*((1 + x)^ (n + 1))*Sum[(k + 1)^n*x^k, {k, 0, Infinity, 2}]; t(n,m)=coefficients(p(x,n),x) EXAMPLE {1}, {1, 0, 1}, {1, 0, 6, 0, 1}, {1, 0, 23, 0, 23, 0, 1}, {1, 0, 76, 0, 230, 0, 76, 0, 1}, {1, 0, 237, 0, 1682, 0, 1682, 0, 237, 0, 1}, {1, 0, 722, 0, 10543, 0, 23548, 0, 10543, 0, 722, 0, 1}, { 1, 0, 2179, 0, 60657, 0, 259723, 0, 259723, 0, 60657, 0, 2179, 0, 1}, {1, 0, 6552, 0, 331612, 0, 2485288, 0, 4675014, 0, 2485288, 0, 331612, 0, 6552, 0, 1}, {1, 0, 19673, 0, 1756340, 0, 21707972, 0, 69413294, 0, 69413294, 0, 21707972, 0, 1756340, 0, 19673, 0, 1}, {1, 0, 59038, 0, 9116141, 0, 178300904, 0, 906923282, 0, 1527092468, 0, 906923282, 0, 178300904, 0, 9116141, 0, 59038, 0, 1} MATHEMATICA Clear[p, x, n, m]; p[x_, n_] = ((1 - x)^ (n + 1))*((1 + x)^ (n + 1))*Sum[(k + 1)^n*x^k, {k, 0, Infinity, 2}]; Table[FullSimplify[ExpandAll[p[x, n]]], {n, 0, 10}]; Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}]; Flatten[%] CROSSREFS Sequence in context: A134899 A076413 A154305 * A293299 A293486 A195398 Adjacent sequences:  A158778 A158779 A158780 * A158782 A158783 A158784 KEYWORD nonn,tabl,uned AUTHOR Roger L. Bagula, Mar 26 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 June 22 18:49 EDT 2021. Contains 345388 sequences. (Running on oeis4.)