The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A322202 G.f.: exp( Sum_{n>=1} A322201(n)*x^n/n ), where A322201(n) is the coefficient of x^n*y^n/(2*n) in Sum_{n>=1} -log(1 - (x^n + y^n)). 4
 1, 2, 7, 20, 63, 190, 613, 1976, 6604, 22368, 77270, 270208, 956780, 3419212, 12323226, 44723840, 163320766, 599601984, 2211844684, 8193734760, 30469278673, 113692852342, 425558528235, 1597428832560, 6011972255226, 22680620270712, 85754229105470, 324898592591960, 1233299357981416, 4689870496585016, 17863799895741982, 68149300647823612, 260364494604701847, 996086232267182566, 3815683108118138847, 14634441964549504036 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Paul D. Hanna, Table of n, a(n) for n = 0..400 FORMULA a(n) ~ c * 4^n / n^(3/2), where c = 2.704933139869066452954644773467... - Vaclav Kotesovec, Jun 18 2019 EXAMPLE G.f.: A(x) = 1 + 2*x + 7*x^2 + 20*x^3 + 63*x^4 + 190*x^5 + 613*x^6 + 1976*x^7 + 6604*x^8 + 22368*x^9 + 77270*x^10 + 270208*x^11 + 956780*x^12 + ... such that log( A(x) ) = 2*x + 10*x^2/2 + 26*x^3/3 + 90*x^4/4 + 262*x^5/5 + 994*x^6/6 + 3446*x^7/7 + 13050*x^8/8 + 48698*x^9/9 + 185310*x^10/10 + ... + A322201(n)*x^n/n + ... sqrt(A(x)) = 1 + x + 3*x^2 + 7*x^3 + 20*x^4 + 54*x^5 + 168*x^6 + 518*x^7 + 1702*x^8 + 5672*x^9 + 19413*x^10 + 67329*x^11 + 236994*x^12 + ... + A322204(n)*x^n + ... PROG (PARI) {L = sum(n=1, 61, -log(1 - (x^n + y^n) +O(x^61) +O(y^61)) ); } {A322201(n) = polcoeff( 2*n*polcoeff( L, n, x), n, y)} {a(n) = polcoeff( exp( sum(m=1, n, A322201(m)*x^m/m ) +x*O(x^n) ), n) } for(n=0, 35, print1( a(n), ", ") ) CROSSREFS Cf. A322200, A322201, A322204. Sequence in context: A014983 A083379 A216246 * A000935 A035071 A055891 Adjacent sequences:  A322199 A322200 A322201 * A322203 A322204 A322205 KEYWORD nonn AUTHOR Paul D. Hanna, Nov 30 2018 STATUS approved

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

Last modified August 9 04:39 EDT 2020. Contains 336319 sequences. (Running on oeis4.)