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!)
 A154630 A triangular sequence of polynomial coefficients: {a,b,c,d}={4, 5, 5, 0}; p(x,n)=(-1)^(n)*(1 - d - c x)^(n + 1)*Sum[(a*k + b)^n*(c*x + d)^k, {k, 0, Infinity}]. 0
 1, -5, 5, 25, 30, 25, -125, -1145, -775, 125, 625, 17180, 50150, 9500, 625, -3125, -201495, -1596850, -1916750, -155625, 3125, 15625, 2110330, 35871175, 120411500, 70354375, 2256250, 15625, -78125, -20789845, -666806625 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Row sums are: {1, 0, 80, -1920, 78080, -3870720, 231034880, -16078110720, 1278679777280, -114405691883520, 11373487802286080} LINKS FORMULA {a,b,c,d}={4, 5, 5, 0}; p(x,n)=(-1)^(n)*(1 - d - c x)^(n + 1)*Sum[(a*k + b)^n*(c*x + d)^k, {k, 0, Infinity}]; t(n,m)=Coefficients(p(x,n)); p(x,n)=(-4)^n*(1-5*n)^(n+1)*LerchPhi[5*x,-n,5/4] EXAMPLE {1}, {-5, 5}, {25, 30, 25}, {-125, -1145, -775, 125}, {625, 17180, 50150, 9500, 625}, {-3125, -201495, -1596850, -1916750, -155625, 3125}, {15625, 2110330, 35871175, 120411500, 70354375,2256250, 15625}, {-78125, -20789845, -666806625, -4737333625, -8100074375, -2518809375, -34296875, 78125}, {390625, 197655480, 11059318300, 143881301000, 525401583750, 508474325000, 89152937500, 511875000, 390625}, {-1953125, -1839446195, -170454627700, -3717803721500, -24702156853750, -52116976906250, -30551523062500, -3137244687500, -7692578125, 1953125}, {9765625, 16896812630, 2501024320325, 86214038005000, 946292721901250, 3649629323762500, 4794767436781250, 1783862843125000, 110088189453125, 115308593750, 9765625} MATHEMATICA Clear[p, a, b, c, d, n]; {a, b, c, d} = {4, 5, 5, 0} p[x_, n_] = (-1)^(n)*(1 - d - c x)^(n + 1)*Sum[(a*k + b)^n*(c*x + d)^k, {k, 0, Infinity}]; 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: A074872 A162962 A170834 * A245520 A245130 A263872 Adjacent sequences:  A154627 A154628 A154629 * A154631 A154632 A154633 KEYWORD sign AUTHOR Roger L. Bagula, Jan 13 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 May 25 17:53 EDT 2020. Contains 334595 sequences. (Running on oeis4.)