A056122 a(n) = (8*n+9)*C(n+8,8)/9.

1, 17, 125, 605, 2255, 7007, 19019, 46475, 104390, 218790, 432718, 814606, 1469650, 2554930, 4299130, 7027834, 11195503, 17425375, 26558675, 39714675, 58363305, 84412185, 120310125, 169169325, 234908700, 322420956, 437766252, 588395500, 783406580, 1033836980

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 (10,-45,120,-210,252,-210,120,-45,10,-1).

Formula

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

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

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

Sum_{n>=0} 1/a(n) = 661396074408/838612775 - 1207959552*Pi/23960365 - 1207959552*sqrt(2)*Pi/23960365 - 9663676416*log(2)/23960365 + 1207959552*sqrt(2)*log(3-2*sqrt(2))/23960365. - Amiram Eldar, Sep 27 2025

Maple

seq((8*n+9)*binomial(n+8, 8)/9, n=0..40); # G. C. Greubel, Aug 29 2019

Mathematica

Table[(8n+9) Binomial[n+8, 8]/9, {n, 0, 40}]  (* Harvey P. Dale, Mar 09 2011 *)

Prog

(PARI) vector(40, n, (8*n+1)*binomial(n+7, 8)/9) \\ G. C. Greubel, Aug 29 2019
(Magma) [(8*n+9)*Binomial(n+8, 8)/9: n in [0..40]]; // G. C. Greubel, Aug 29 2019
(SageMath) [(8*n+9)*binomial(n+8, 8)/9 for n in (0..40)] # G. C. Greubel, Aug 29 2019
(GAP) List([0..40], n-> (8*n+9)*Binomial(n+8, 8)/9); # G. C. Greubel, Aug 29 2019

Crossrefs

Partial sums of A056001.

Cf. A056001, A093565 ((8, 1) Pascal, column m=9).

Cf. similar sequences listed in A254142.

Sequence in context: A196336 A297975 A023081 * A036828 A142613 A066453

Adjacent sequences: A056119 A056120 A056121 * A056123 A056124 A056125

Keyword

easy,nonn

Author

Barry E. Williams, Jul 06 2000

Status

approved