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!)
 A056125 a(n) = (5*n + 4)*binomial(n+7,7)/4. 2
 1, 18, 126, 570, 1980, 5742, 14586, 33462, 70785, 140140, 262548, 469404, 806208, 1337220, 2151180, 3368244, 5148297, 7700814, 11296450, 16280550, 23088780, 32265090, 44482230, 60565050, 81516825, 108548856, 143113608, 186941656 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1). FORMULA G.f.: (1+9*x)/(1-x)^9. a(0)=1, a(1)=18, a(2)=126, a(3)=570, a(4)=1980, a(5)=5742, a(6)=14586, a(7)=33462, a(8)=70785, a(n) = 9*a(n-1) -36*a(n-2) +84*a(n-3) -126*a(n-4) + 126*a(n-5) -84*a(n-6) +36*a(n-7) -9*a(n-8) +a(n-9). - Harvey P. Dale, Jan 18 2013 From G. C. Greubel, Jan 19 2020: (Start) a(n) = 10*binomial(n+8,8) - 9*binomial(n+7,7). E.g.f.: (20160 + 342720*x + 917280*x^2 + 823200*x^3 + 323400*x^4 + 62328*x^5 + 6076*x^6 + 284*x^7 + 5*x^8)*exp(x)/20160. (End) MAPLE seq( (5*n+4)*binomial(n+7, 7)/4, n=0..30); # G. C. Greubel, Jan 19 2020 MATHEMATICA Table[((5n+4)Binomial[n+7, 7])/4, {n, 0, 30}] (* or *) LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {1, 18, 126, 570, 1980, 5742, 14586, 33462, 70785}, 30] (* Harvey P. Dale, Jan 18 2013 *) PROG (PARI) vector(31, n, (5*n-1)*binomial(n+6, 7)/4 ) \\ G. C. Greubel, Jan 19 2020 (MAGMA) [(5*n+4)*Binomial(n+7, 7)/4: n in [0..30]]; // G. C. Greubel, Jan 19 2020 (Sage) [(5*n+4)*binomial(n+7, 7)/4 for n in (0..30)] # G. C. Greubel, Jan 19 2020 (GAP) List([0..30], n-> (5*n+4)*Binomial(n+7, 7)/4 ); # G. C. Greubel, Jan 19 2020 CROSSREFS Cf. A052254. Cf. A093645 ((10, 1) Pascal, column m=8). Partial sums of A052254. Sequence in context: A002424 A101378 A107417 * A223212 A297027 A027566 Adjacent sequences:  A056122 A056123 A056124 * A056126 A056127 A056128 KEYWORD easy,nonn AUTHOR Barry E. Williams, Jul 07 2000 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 April 14 21:21 EDT 2021. Contains 342962 sequences. (Running on oeis4.)