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a(n) = (8*n+9)*C(n+8,8)/9.
3

%I #24 Sep 08 2022 08:45:01

%S 1,17,125,605,2255,7007,19019,46475,104390,218790,432718,814606,

%T 1469650,2554930,4299130,7027834,11195503,17425375,26558675,39714675,

%U 58363305,84412185,120310125,169169325,234908700,322420956,437766252

%N a(n) = (8*n+9)*C(n+8,8)/9.

%H G. C. Greubel, <a href="/A056122/b056122.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: (1+7*x)/(1-x)^10.

%F a(n) = (362880 + 1308816*n + 1939788*n^2 + 1550548*n^3 + 740313*n^4 + 220416*n^5 + 41202*n^6 + 4692*n^7 + 297*n^8 + 8*n^9)/362880. - _Harvey P. Dale_, Mar 09 2011

%F E.g.f.: (362880 +5806080*x +16692480*x^2 +16934400*x^3 +7832160*x^4 + 1862784*x^5 +239904 x^6 +16704*x^7 +585*x^8 +8*x^9)*exp(x)/362880. - _G. C. Greubel_, Aug 29 2019

%p seq((8*n+9)*binomial(n+8,8)/9, n=0..40); # _G. C. Greubel_, Aug 29 2019

%t Table[(8n+9) Binomial[n+8,8]/9,{n,0,40}] (* _Harvey P. Dale_, Mar 09 2011 *)

%o (PARI) vector(40, n, (8*n+1)*binomial(n+7,8)/9) \\ _G. C. Greubel_, Aug 29 2019

%o (Magma) [(8*n+9)*Binomial(n+8,8)/9: n in [0..40]]; // _G. C. Greubel_, Aug 29 2019

%o (Sage) [(8*n+9)*binomial(n+8,8)/9 for n in (0..40)] # _G. C. Greubel_, Aug 29 2019

%o (GAP) List([0..40], n-> (8*n+9)*Binomial(n+8,8)/9); # _G. C. Greubel_, Aug 29 2019

%Y Cf. A056001.

%Y Cf. A093565 ((8, 1) Pascal, column m=9). Partial sums of A056001.

%Y Cf. similar sequences listed in A254142.

%K easy,nonn

%O 0,2

%A _Barry E. Williams_, Jul 06 2000