This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A062990 Eighth column (r=7) of FS(5) staircase array A062985. 2
 5, 30, 110, 315, 771, 1688, 3396, 6390, 11385, 19382, 31746, 50297, 77415, 116160, 170408, 245004, 345933, 480510, 657590, 887799, 1183787, 1560504, 2035500, 2629250, 3365505, 4271670, 5379210, 6724085, 8347215 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS In the Frey-Sellers reference this sequence is called {(n+2) over 7}_{4}, n >= 0. LINKS Harry J. Smith, Table of n, a(n) for n = 0..1000 D. D. Frey and J. A. Sellers, Generalizing Bailey's generalization of the Catalan numbers, The Fibonacci Quarterly, 39 (2001) 142-148. Index entries for linear recurrences with constant coefficients, signature (8, -28, 56, -70, 56, -28, 8, -1). FORMULA a(n) = A062985(n+2, 7) = (n+1)*(n+2)*(n+3)*(n^4 + 29*n^3 + 326*n^2 + 1744*n + 4200)/7!. G.f.: N(5;1, x)/(1-x)^8 with N(5;1, x)= 5-10*x+10*x^2-5*x^3+x^4 = (1-(1-x)^5)/x polynomial of second row of A062986. a(n) = binomial(n+7,n) - binomial(n+2,n)). - Zerinvary Lajos, Jun 23 2006 MAPLE [seq((binomial(n+7, n)-binomial(n+2, n)), n=1..29)]; # Zerinvary Lajos, Jun 23 2006 MATHEMATICA Table[Binomial[n+7, n]-Binomial[n+2, n], {n, 30}] (* or *) LinearRecurrence[ {8, -28, 56, -70, 56, -28, 8, -1}, {5, 30, 110, 315, 771, 1688, 3396, 6390}, 30] (* Harvey P. Dale, Jun 09 2016 *) PROG (PARI) { for (n=0, 1000, m=n + 1; a=binomial(m + 7, m) - binomial(m + 2, m); write("b062990.txt", n, " ", a) ) } \\ Harry J. Smith, Aug 15 2009 CROSSREFS Partial sums of A062989. Sequence in context: A071252 A174002 A030506 * A018213 A047661 A000649 Adjacent sequences:  A062987 A062988 A062989 * A062991 A062992 A062993 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Jul 12 2001 EXTENSIONS More terms from Zerinvary Lajos, Jun 23 2006 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 March 23 02:53 EDT 2019. Contains 321422 sequences. (Running on oeis4.)