A010979 - OEIS

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A010979

Binomial coefficient C(n,26).

1, 27, 378, 3654, 27405, 169911, 906192, 4272048, 18156204, 70607460, 254186856, 854992152, 2707475148, 8122425444, 23206929840, 63432274896, 166509721602, 421171648758, 1029530696964, 2438362177020, 5608233007146, 12551759587422, 27385657281648

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OFFSET

26,2

LINKS

T. D. Noe, Table of n, a(n) for n = 26..1000

Index entries for linear recurrences with constant coefficients, signature (27, -351, 2925, -17550, 80730, -296010, 888030, -2220075, 4686825, -8436285, 13037895, -17383860, 20058300, -20058300, 17383860, -13037895, 8436285, -4686825, 2220075, -888030, 296010, -80730, 17550, -2925, 351, -27, 1).

FORMULA

G.f.: x^26/(1-x)^27. - Zerinvary Lajos, Aug 18 2008; adapted to offset by Enxhell Luzhnica, Jan 21 2017

From Amiram Eldar, Dec 11 2020: (Start)

Sum_{n>=26} 1/a(n) = 26/25.

Sum_{n>=26} (-1)^n/a(n) = A001787(26)*log(2) - A242091(26)/25! = 872415232*log(2) - 155661889283343139/257414850 = 0.9653663105... (End)

MAPLE

seq(binomial(n, 26), n=26..41); # Zerinvary Lajos, Aug 18 2008

MATHEMATICA

Table[Binomial[n, 26], {n, 26, 60}] (* Vladimir Joseph Stephan Orlovsky, Apr 26 2011 *)

PROG

(Magma) [Binomial(n, 26): n in [26..60]]; // Vincenzo Librandi, Jun 12 2013

(PARI) x='x+O('x^50); Vec(x^26/(1-x)^27) \\ G. C. Greubel, Nov 23 2017