This site is supported by donations to The OEIS Foundation.



(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A279619 Expansion of g.f. of A002652 in powers of the g.f. of A279618. 36
1, 2, 22, 336, 6006, 117348, 2428272, 52303680, 1160427510, 26337699740, 608642155660, 14272471122560, 338764038330480, 8123136091556640, 196484811079765440, 4788469475873867520, 117465323079289162230, 2898183118626011393100 (list; graph; refs; listen; history; text; internal format)



G.f. is the square root of the g.f. for A183204.

This sequence is c_n in Theorem 6.1 in O'Brien's thesis.

Also see Conjecture 5.4 in Chan, Cooper and Sica's paper.


L. O'Brien, Modular forms and two new integer sequences at level 7, Massey University, 2016.


Table of n, a(n) for n=1..18.

H. H. Chan, S. Cooper, F. Sica, Congruences satisfied by Apéry-like numbers, International Journal of Number Theory, 2010, 6(01), 89-97. Conjecture 5.4.

Lynette O'Brien, Modular forms and two new integer sequences at level 7

Lynette O'Brien, Modular forms and two new integer sequences at level 7


(n+1)^2a_7(n+1)=(26*n^2+13*n+2)a_7(n)+3*(3*n-1)*(3*n-2)a_7(n-1), a(0)=1, a(-1)=0.

Conjecture: For any positive integer n and any prime p with p equiv. 0,1,2 or 4 modulo 7, a(n) equiv. a(n)=a(n_0)a(n_1)...a(n_r) modulo p, where n=n_0+n_1p+...n_rp^r is the base p representation of n.

Conjecture: a(n)~ C n^(-3/2) 27^n where C=0.0955223052681267146513079107870296256727946666510071798669948234917659...


G.f. = 1 + 2*x + 22*x^2 + 336*x^3 + 6006*x^4 + ....


Cf. A183204, A279613, A279618.

The Apéry-like numbers [or Apéry-like sequences, Apery-like numbers, Apery-like sequences] include A000172, A000984, A002893, A002895, A005258, A005259, A005260, A006077, A036917, A063007, A081085, A093388, A125143 (apart from signs), A143003, A143007, A143413, A143414, A143415, A143583, A183204, A214262, A219692, A226535, A227216, A227454, A229111 (apart from signs), A260667, A260832, A262177, A264541, A264542, A279619, A290575, A290576. (The term "Apery-like" is not well-defined.)

Sequence in context: A256928 A266888 A155674 * A245113 A078232 A151615

Adjacent sequences:  A279616 A279617 A279618 * A279620 A279621 A279622




Lynette O'Brien, Dec 15 2016



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 19 06:46 EST 2018. Contains 299330 sequences. (Running on oeis4.)