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

Author

Clark Kimberling

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

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.

Programs

GAP

List([0..35], n-> (7*n+1)*Binomial(n+6,7)/8); # G. C. Greubel, Aug 29 2019

Magma

[0] cat [(7*n+8)*Binomial(n+7, 7)/8: n in [0..30]]; // Vincenzo Librandi, Mar 20 2015

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 *)

PARI

lista(nn) = for (n=0, nn, print1((7*n+1)*binomial(n+6,7)/8, ", ")); \\ Michel Marcus, Mar 20 2015

Sage

[(7*n+1)*binomial(n+6,7)/8 for n in (0..35)] # G. C. Greubel, Aug 29 2019

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!

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