The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A363557 Expansion of g.f. A(x) satisfying 0 = Sum_{n>=0} (-1)^n * x^(n*(n-1)/2) * A(x)^n / Product_{k=1..n+1} (1 - x^k). 1
 1, 1, 1, 2, 4, 9, 20, 47, 112, 273, 677, 1702, 4330, 11128, 28847, 75341, 198066, 523713, 1391869, 3716098, 9962252, 26806275, 72372721, 195994320, 532266707, 1449216287, 3955193019, 10818202369, 29650108510, 81417795070, 223964216673, 617097850848, 1702943168118 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Related identities: (1) 0 = Sum_{n>=0} (-1)^n * x^(n*(n-1)/2) * B(x)^n / Product_{k=1..n+1} (1 - x^k*B(x)), where B(x) = 1/(1-x). (2) 1 = Sum_{n>=0} (-1)^n * x^(n*(n+1)/2) / Product_{k=1..n+1} (1 - x^k). LINKS Paul D. Hanna, Table of n, a(n) for n = 0..500 FORMULA G.f. A(x) = Sum_{n>=0} a(n)*x^n may be defined by the following. (1) 0 = Sum_{n>=0} (-1)^n * x^(n*(n-1)/2) * A(x)^n / Product_{k=1..n+1} (1 - x^k). (2) 1/(A(x) - x) = Sum_{n>=0} (-1)^n * x^(n*(n+1)/2) * A(x)^n / Product_{k=1..n+1} (1 - x^k). EXAMPLE G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 4*x^4 + 9*x^5 + 20*x^6 + 47*x^7 + 112*x^8 + 273*x^9 + 677*x^10 + 1702*x^11 + 4330*x^12 + ... PROG (PARI) {a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0); A[#A] = polcoeff( sum(m=0, 2*sqrtint(#A), (-1)^m * (x)^(m*(m-1)/2) * Ser(A)^m / prod(k=1, m+1, (1 - x^k +x*O(x^#A) ) )), #A-1); ); A[n+1]} for(n=0, 32, print1(a(n), ", ")) CROSSREFS Cf. A082395, A363555. Sequence in context: A003018 A196244 A035084 * A213905 A058385 A058386 Adjacent sequences: A363554 A363555 A363556 * A363558 A363559 A363560 KEYWORD nonn AUTHOR Paul D. Hanna, Jul 11 2023 STATUS approved

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

Last modified April 23 16:28 EDT 2024. Contains 371916 sequences. (Running on oeis4.)