A053367 Partial sums of A050494.

1, 11, 63, 255, 825, 2277, 5577, 12441, 25740, 50050, 92378, 163098, 277134, 455430, 726750, 1129854, 1716099, 2552517, 3725425, 5344625, 7548255, 10508355, 14437215, 19594575, 26295750, 34920756, 45924516, 59848228, 77331980, 99128700, 126119532, 159330732, 199952181, 249357615

Offset: 0

Author

Barry E. Williams, Jan 06 2000

Keywords

• easy
• nonn

References

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Crossrefs

Cf. A050494.

Cf. A093560 ((3, 1) Pascal, column m=8).

Programs

Magma

[(3*n+8)*Binomial(n+7,7)/8: n in [0..30]]; // G. C. Greubel, May 25 2018

Mathematica

LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {1, 11, 63, 255, 825, 2277, 5577, 12441, 25740}, 30] (* or *) Table[(3*n+8)* Binomial[n+7,7]/8, {n,0,30}] (* G. C. Greubel, May 25 2018 *)

PARI

a(n)=binomial(n+7, 7)*(3*n+8)/8 \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = binomial(n+7, 7)*(3n+8)/8.

G.f.: (1+2*x)/(1-x)^9.

Extensions

Terms a(24) onward added by G. C. Greubel, May 25 2018