A034266 Partial sums of A027818.

0, 1, 15, 99, 435, 1485, 4257, 10725, 24453, 51480, 101530, 189618, 338130, 579462, 959310, 1540710, 2408934, 3677355, 5494401, 8051725, 11593725, 16428555, 22940775, 31605795, 43006275, 57850650, 76993956, 101461140, 132473044, 171475260, 220170060, 280551612

Offset

0,3

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

Formula

a(n) = (7*n+1)*binomial(n+6, 7)/8.

G.f.: x*(1+6*x)/(1-x)^9.

E.g.f.: x*(8! +262080*x +383040*x^2 +210000*x^3 +52080*x^4 +6216*x^5 + 344*x^6 +7*x^7)*exp(x)/8!

Maple

f:=n->(7*n+8)*binomial(n+7, 7)/8; [seq(f(n), n=-1..40)]; # N. J. A. Sloane, Mar 25 2015

Mathematica

CoefficientList[Series[x(1+6x)/(1-x)^9, {x, 0, 30}], x] (* Vincenzo Librandi, Mar 20 2015 *)
Table[(7*n+1)*Binomial[n+6, 7]/8, {n, 0, 35}] (* G. C. Greubel, Aug 29 2019 *)

Prog

(PARI) lista(nn) = for (n=0, nn, print1((7*n+1)*binomial(n+6, 7)/8, ", ")); \\ Michel Marcus, Mar 20 2015
(Magma) [0] cat [(7*n+8)*Binomial(n+7, 7)/8: n in [0..30]]; // Vincenzo Librandi, Mar 20 2015
(Sage) [(7*n+1)*binomial(n+6, 7)/8 for n in (0..35)] # G. C. Greubel, Aug 29 2019
(GAP) List([0..35], n-> (7*n+1)*Binomial(n+6, 7)/8); # G. C. Greubel, Aug 29 2019

Crossrefs

a(n)=f(n, 6) where f is given in A034261.

Cf. A027818, A053367, A034266.

Cf. A093564 ((7, 1) Pascal, column m=8).

Cf. similar sequences listed in A254142.

Sequence in context: A341396 A307158 A000973 * A087661 A319777 A242657

Adjacent sequences: A034263 A034264 A034265 * A034267 A034268 A034269

Keyword

easy,nonn

Author

Clark Kimberling

Extensions

Better description from Barry E. Williams, Jan 25 2000

Corrected and extended by N. J. A. Sloane, Apr 21 2000

More terms from Michel Marcus, Mar 20 2015

Status

approved