A227026 Numbers k such that k!/m! is a triangular number for some m < k-1.

3, 5, 6, 7, 11, 14, 15, 58, 85, 493, 638, 2871, 16731, 97513, 568345, 3312555, 19306983, 112529341, 655869061, 3822685023, 22280241075, 129858761425, 756872327473, 4411375203411, 25711378892991, 149856898154533, 873430010034205, 5090723162050695

Offset: 1

Author

Alex Ratushnyak, Jun 27 2013

Keywords

• nonn
• easy

Comments

A011900 is a subsequence, except A011900(0)=1.

According to Melissen's comment in A097571, m > k-7.

Links

• Index entries for linear recurrences with constant coefficients, signature (7,-7,1).

Crossrefs

Cf. A000217, A011900, A097571.

Programs

Mathematica

CoefficientList[Series[(3 - 16 x - 8 x^2 - 3 x^3 - x^4 - 20 x^5 - 13 x^6 + 40 x^7 - 230 x^8 + 289 x^9 - 2276 x^10 + 1771 x^11 + 607 x^12 - 145 x^13) / ((1 - x) (1 - 6 x + x^2)), {x, 0, 30}], x] (* Bruno Berselli, Jun 28 2013 *)

Formula

a(n) = 7a(n-1) - 7a(n-2) + a(n-3) for n > 14. - Charles R Greathouse IV, Jun 28 2013

G.f.: x * (3 -16*x -8*x^2 -3*x^3 -x^4 -20*x^5 -13*x^6 +40*x^7 -230*x^8 +289*x^9 -2276*x^10 +1771*x^11 +607*x^12 -145*x^13) / ((1-x)*(1-6*x+x^2)). - Bruno Berselli, Jun 28 2013