A088626 a(n) = 42*binomial(n,10). (Formerly N2296)

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 42, 462, 2772, 12012, 42042, 126126, 336336, 816816, 1837836, 3879876, 7759752, 14814072, 27159132, 48050772, 82372752, 137287920, 223092870, 354323970, 551170620, 841260420, 1261890630, 1862790930, 2709514080, 3887563680

Offset

0,11

References

Charles Jordan, Calculus of Finite Differences, Chelsea, 1965, p. 449.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Formula

G.f.: 42*x^10/(1-x)^11. - Colin Barker, Oct 30 2012

From Amiram Eldar, Sep 28 2025: (Start)

Sum_{n>=10} 1/a(n) = 5/189.

Sum_{n>=10} (-1)^n/a(n) = 2560*log(2)/21 - 447047/5292. (End)

Mathematica

42Binomial[Range[0, 40], 10] (* Harvey P. Dale, Apr 19 2020 *)

Prog

(PARI) a(n)=42*binomial(n, 10) \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

A diagonal of A088617.

Sequence in context: A244909 A090297 A008387 * A328175 A216109 A216111

Adjacent sequences: A088623 A088624 A088625 * A088627 A088628 A088629

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 23 2003

Status

approved