A034266 - OEIS

%I #31 Sep 08 2022 08:44:51

%S 0,1,15,99,435,1485,4257,10725,24453,51480,101530,189618,338130,

%T 579462,959310,1540710,2408934,3677355,5494401,8051725,11593725,

%U 16428555,22940775,31605795,43006275,57850650,76993956,101461140,132473044,171475260,220170060,280551612

%N Partial sums of A027818.

%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, N. Y., 1964, pp. 194-196.

%H G. C. Greubel, <a href="/A034266/b034266.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = (7*n+1)*binomial(n+6, 7)/8.

%F G.f.: x*(1+6*x)/(1-x)^9.

%F E.g.f.: x*(8! +262080*x +383040*x^2 +210000*x^3 +52080*x^4 +6216*x^5 + 344*x^6 +7*x^7)*exp(x)/8!

%p f:=n->(7*n+8)*binomial(n+7, 7)/8; [seq(f(n),n=-1..40)]; # _N. J. A. Sloane_, Mar 25 2015

%t CoefficientList[Series[x(1+6x)/(1-x)^9, {x, 0, 30}], x] (* _Vincenzo Librandi_, Mar 20 2015 *)

%t Table[(7*n+1)*Binomial[n+6,7]/8, {n,0,35}] (* _G. C. Greubel_, Aug 29 2019 *)

%o (PARI) lista(nn) = for (n=0, nn, print1((7*n+1)*binomial(n+6,7)/8, ", ")); \\ _Michel Marcus_, Mar 20 2015

%o (Magma) [0] cat [(7*n+8)*Binomial(n+7, 7)/8: n in [0..30]]; // _Vincenzo Librandi_, Mar 20 2015

%o (Sage) [(7*n+1)*binomial(n+6,7)/8 for n in (0..35)] # _G. C. Greubel_, Aug 29 2019

%o (GAP) List([0..35], n-> (7*n+1)*Binomial(n+6,7)/8); # _G. C. Greubel_, Aug 29 2019

%Y a(n)=f(n, 6) where f is given in A034261.

%Y Cf. A027818, A053367, A034266.

%Y Cf. A093564 ((7, 1) Pascal, column m=8).

%Y Cf. similar sequences listed in A254142.

%K easy,nonn

%O 0,3

%A _Clark Kimberling_

%E Better description from _Barry E. Williams_, Jan 25 2000

%E Corrected and extended by _N. J. A. Sloane_, Apr 21 2000

%E More terms from _Michel Marcus_, Mar 20 2015