This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A081178 a(0)=1; for n>=1, a(n) = sum(7^k*N(n,k), k=0..n), where N(n,k)=1/n*C(n,k)*C(n,k+1) are the Narayana numbers (A001263). 8
 1, 1, 8, 71, 680, 6882, 72528, 788019, 8766248, 99362894, 1143498224, 13326176998, 156950554384, 1865210341828, 22338852956064, 269355965364459, 3267146912972328, 39837475762660374, 488032452193307568 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS More generally, coefficients of (1+m*x-sqrt(m^2*x^2-(2*m+4)*x+1))/((2*m+2)*x) are given by: a(n) = sum(k=0..n, (m+1)^k*N(n,k)). The Hankel transform of this sequence is 7^C(n+1,2). - Philippe Deléham, Oct 29 2007 a(n) = upper left term in M^n, M = the production matrix: 1, 1 7, 7, 7 1, 1, 1, 1 7, 7, 7, 7, 7 1, 1, 1, 1, 1, 1 ... - Gary W. Adamson, Jul 08 2011 Shifts left when INVERT transform applied seven times. - Benedict W. J. Irwin, Feb 07 2016 G.f.: 1/(1 - x/(1 - 7*x/(1 - x/(1 - 7*x/(1 - x/(1 - ...)))))), a continued fraction. - Ilya Gutkovskiy, Apr 21 2017 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 Paul Barry, On Integer-Sequence-Based Constructions of Generalized Pascal Triangles, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.4. FORMULA G.f.: (1+6*x-sqrt(36*x^2-16*x+1))/(14*x). a(n) = (8(2n-1)a(n-1) - 36(n-2)a(n-2))/(n+1) for n>=2, a(0)=a(1)=1. - Philippe Deléham, Aug 19 2005 a(n) ~ sqrt(14+8*sqrt(7))*(8+2*sqrt(7))^n/(14*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 13 2012 MAPLE A081178_list := proc(n) local j, a, w; a := array(0..n); a[0] := 1; for w from 1 to n do a[w] := a[w-1]+7*add(a[j]*a[w-j-1], j=1..w-1) od; convert(a, list) end: A081178_list(18); # Peter Luschny, May 19 2011 MATHEMATICA Table[SeriesCoefficient[(1+6*x-Sqrt[36*x^2-16*x+1])/(14*x), {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 13 2012 *) PROG (PARI) a(n)=if(n<1, 1, sum(k=0, n, 7^k/n*binomial(n, k)*binomial(n, k+1))) CROSSREFS Cf. A001003, A007564, A059231. Sequence in context: A187709 A292865 A152265 * A096341 A199687 A225033 Adjacent sequences:  A081175 A081176 A081177 * A081179 A081180 A081181 KEYWORD nonn AUTHOR Benoit Cloitre, May 10 2003 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 18 19:06 EST 2017. Contains 294894 sequences.