This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A178640 Triangle T(n,k) with the coefficient [x^k] of the series (-1)^(n+1) * (x-1)^(n+1) * Sum_{j>=0} (5+8*j)^n*x^j in row n, column k. 1
 1, 5, 3, 25, 94, 9, 125, 1697, 1223, 27, 625, 25436, 57926, 14236, 81, 3125, 352543, 1903218, 1513438, 159593, 243, 15625, 4717434, 52306583, 95276588, 34660263, 1766458, 729, 78125, 62123517, 1301287905, 4593751457, 3854897607, 738035607 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Row sums are 1, 8, 128, 3072, 98304, 3932160, 188743680, 10569646080, 676457349120, 48704929136640, 3896394330931200, .... Other pairs of consecutive Fibonacci numbers could be substituted for the two main parameters (5,8) in the definition. Using the pair (0,1) or (1,1) yields A008292. Using the pair (1,2) yields A060187. LINKS FORMULA T(n,0) = 5^n = A000351(n). EXAMPLE 1; 5, 3; 25, 94, 9; 125, 1697, 1223, 27; 625, 25436, 57926, 14236, 81; 3125, 352543, 1903218, 1513438, 159593, 243; 15625, 4717434, 52306583, 95276588, 34660263, 1766458, 729; 78125, 62123517, 1301287905, 4593751457, 3854897607, 738035607, 19469675, 2187; 390625, 812215096, 30495345372, 189174172168, 303412512454, 137293837704, 15054569308, 214299832, 6561; MAPLE A178640 := proc(n, k) (-1)^(n+1)*(x-1)^(n+1)*add( (5+8*j)^n*x^j, j=0..k) ; coeftayl(%, x=0, k) ; end proc: # R. J. Mathar, Apr 05 2011 MATHEMATICA Clear[m, m0, t, n, k] m0 = {{1, 1}, {1, 0}} m[l_] := MatrixPower[m0, l] t[l_, k_] = If[l == 0, 1, m[l][[1, 1]]*k + m[l][[1, 2]]] p[x_, n_, l_] := (-1)^(n + 1)*(-1 + x)^(n + 1)*Sum[t[l, k]^ n*x^k, {k, 0, Infinity}] Table[Flatten[Table[CoefficientList[FullSimplify[ExpandAll[p[x, n, l]]], x], {n, 0, 10}]], {l, 0, 10}] CROSSREFS Sequence in context: A032532 A111108 A038245 * A273153 A288812 A288898 Adjacent sequences:  A178637 A178638 A178639 * A178641 A178642 A178643 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, May 31 2010 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 September 16 18:56 EDT 2019. Contains 327117 sequences. (Running on oeis4.)