cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 11-13 of 13 results.

A034266 Partial sums of A027818.

Original entry on oeis.org

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

Views

Author

Clark Kimberling

Keywords

References

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

Links

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

A050403 Partial sums of A051877.

Original entry on oeis.org

1, 13, 70, 252, 714, 1722, 3696, 7260, 13299, 23023, 38038, 60424, 92820, 138516, 201552, 286824, 400197, 548625, 740278, 984676, 1292830, 1677390, 2152800, 2735460, 3443895, 4298931, 5323878, 6544720, 7990312, 9692584, 11686752, 14011536, 16709385, 19826709, 23414118, 27526668
Offset: 0

Views

Author

Barry E. Williams, Dec 21 1999

Keywords

References

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

Links

Crossrefs

Cf. A051877.
Cf. A093564 ((7, 1) Pascal, column m=6).

Programs

  • GAP
    List([0..30], n-> (7*n+6)*Binomial(n+5, 5)/6); # G. C. Greubel, Aug 29 2019
  • Magma
    [(7*n+6)*Binomial(n+5, 5)/6: n in [0..30]]; // G. C. Greubel, Aug 29 2019
  • Maple
    Seq((7*n+6)*binomial(n+5, 5)/6, n=0..30); # G. C. Greubel, Aug 29 2019
  • Mathematica
    Table[(7*n+6)*Binomial[n+5, 5]/6, {n,0,30}] (* G. C. Greubel, Aug 29 2019 *)
  • PARI
    a(n) = binomial(n+5,5)*(7*n+6)/6; \\ Michel Marcus, Jan 09 2015
  • Sage
    [(7*n+6)*binomial(n+5, 5)/6 for n in (0..30)] # G. C. Greubel, Aug 29 2019

Formula

a(n) = C(n+5, 5)*(7*n+6)/6.
G.f.: (1+6*x)/(1-x)^7.
E.g.f.: (5! +8640*x +16200*x^2 +9600*x^3 +2250*x^4 +216*x^5 +7*x^6 )*exp(x)/5!. - G. C. Greubel, Aug 29 2019

Extensions

Corrected by T. D. Noe, Nov 09 2006
Terms a(28) onward added by G. C. Greubel, Aug 29 2019

A055994 Expansion of (1+6x)/(1-x)^10.

Original entry on oeis.org

1, 16, 115, 550, 2035, 6292, 17017, 41470, 92950, 194480, 384098, 722228, 1301690, 2261000, 3801710, 6210644, 9887999, 15382400, 23434125, 35027850, 51456405, 74397180, 106002975, 149009250, 206859900, 283853856, 385314996, 517788040
Offset: 0

Views

Author

Barry E. Williams, Jun 04 2000

Keywords

Comments

Partial sums of A034266. - Vladimir Joseph Stephan Orlovsky, Jun 25 2009

References

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

Links

Crossrefs

Cf. A034266.
Cf. A093564 ((7, 1) Pascal, column m=9). Partial sums of A034266.

Programs

  • Magma
    [((7*n+9)*Binomial(n+8,8))/9: n in [0..40]]; // Vincenzo Librandi, Jul 30 2014
  • Mathematica
    CoefficientList[Series[(1 + 6 x)/(1 - x)^10, {x, 0, 50}], x] (* Vincenzo Librandi, Jul 30 2014 *)
LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{1,16,115,550,2035,6292,17017,41470,92950,194480},30] (* Harvey P. Dale, Sep 07 2022 *)

Formula

a(n) = (7n+9)*C(n+8, 8)/9.
G.f.: (1+6x)/(1-x)^10.
Previous Showing 11-13 of 13 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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