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Partial sums of A051877.
3

%I #25 Sep 08 2022 08:44:58

%S 1,13,70,252,714,1722,3696,7260,13299,23023,38038,60424,92820,138516,

%T 201552,286824,400197,548625,740278,984676,1292830,1677390,2152800,

%U 2735460,3443895,4298931,5323878,6544720,7990312,9692584,11686752,14011536,16709385,19826709,23414118,27526668

%N Partial sums of A051877.

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

%H G. C. Greubel, <a href="/A050403/b050403.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).

%F a(n) = C(n+5, 5)*(7*n+6)/6.

%F G.f.: (1+6*x)/(1-x)^7.

%F E.g.f.: (5! +8640*x +16200*x^2 +9600*x^3 +2250*x^4 +216*x^5 +7*x^6 )*exp(x)/5!. - _G. C. Greubel_, Aug 29 2019

%p Seq((7*n+6)*binomial(n+5, 5)/6, n=0..30); # _G. C. Greubel_, Aug 29 2019

%t Table[(7*n+6)*Binomial[n+5, 5]/6, {n,0,30}] (* _G. C. Greubel_, Aug 29 2019 *)

%o (PARI) a(n) = binomial(n+5,5)*(7*n+6)/6; \\ _Michel Marcus_, Jan 09 2015

%o (Magma) [(7*n+6)*Binomial(n+5, 5)/6: n in [0..30]]; // _G. C. Greubel_, Aug 29 2019

%o (Sage) [(7*n+6)*binomial(n+5, 5)/6 for n in (0..30)] # _G. C. Greubel_, Aug 29 2019

%o (GAP) List([0..30], n-> (7*n+6)*Binomial(n+5, 5)/6); # _G. C. Greubel_, Aug 29 2019

%Y Cf. A051877.

%Y Cf. A093564 ((7, 1) Pascal, column m=6).

%K easy,nonn

%O 0,2

%A _Barry E. Williams_, Dec 21 1999

%E Corrected by _T. D. Noe_, Nov 09 2006

%E Terms a(28) onward added by _G. C. Greubel_, Aug 29 2019