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%I #20 Sep 08 2022 08:46:11
%S 1,19,154,814,3289,11011,32032,83512,199342,442442,923780,1830764,
%T 3468374,6317234,11113784,18958808,31461815,50930165,80613390,
%U 125014890,190285095,284712285,419329560,608658960,871616460,1232604516,1722822024,2381824984
%N a(n) = (9*n+10)*binomial(n+9,9)/10.
%C Partial sums of A056003.
%C If n is of the form 8*k+2*(-1)^k-1 or 8*k+2*(-1)^k-2 then a(n) is odd.
%H Bruno Berselli, <a href="/A254142/b254142.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
%F G.f.: (1 + 8*x)/(1-x)^11.
%F a(n) = Sum_{i=0..n} (i+1)*A000581(i+8).
%F a(n+1) = 8*A001287(n+10) + A001287(n+11).
%p seq((9*n+10)*binomial(n+9,9)/10, n=0..30); # _G. C. Greubel_, Aug 28 2019
%t Table[(9n+10)Binomial[n+9, 9]/10, {n, 0, 30}]
%o (PARI) vector(30, n, n--; (9*n+10)*binomial(n+9, 9)/10)
%o (Sage) [(9*n+10)*binomial(n+9,9)/10 for n in (0..30)]
%o (Magma) [(9*n+10)*Binomial(n+9,9)/10: n in [0..30]];
%o (GAP) List([0..30], n-> (9*n+10)*Binomial(n+9,9)/10); # _G. C. Greubel_, Aug 28 2019
%Y Cf. A000581, A001287, A056003.
%Y Cf. sequences of the type (k*n+k+1)*binomial(n+k,k)/(k+1): A000217 (k=1), A000330 (k=2), A001296 (k=3), A034263 (k=4), A051946 (k=5), A034265 (k=6), A034266 (k=7), A056122 (k=8), this sequence (k=9).
%K nonn,easy
%O 0,2
%A _Bruno Berselli_, Jan 26 2015
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