This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A261608 G.f.: Sum_{n=-oo..+oo, n<>0} x^(n^2) / (1 - x^n)^(n+1). 4
 2, 1, 4, 5, 6, 6, 8, 16, 12, 15, 12, 32, 14, 28, 32, 52, 18, 55, 20, 74, 72, 66, 24, 160, 28, 91, 140, 146, 30, 205, 32, 271, 244, 153, 72, 442, 38, 190, 392, 563, 42, 518, 44, 505, 788, 276, 48, 1510, 52, 451, 852, 896, 54, 1086, 728, 1748, 1180, 435, 60, 3291, 62, 496, 1648, 2867, 1848, 2101, 68, 2481, 2072, 1953, 72, 7634 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Paul D. Hanna, Table of n, a(n) for n = 1..1000 FORMULA G.f.: Sum_{n=-oo..+oo, n<>0} x^n * (x^n - 1)^(n-1). G.f.: Sum_{n=-oo..+oo} x^(n^2)/(1 + x^n)^n, where the sum is taken to exclude the coefficient of x^0. G.f.: Sum_{n=-oo..+oo} (1 + x^n)^n, where the sum is taken to exclude the coefficient of x^0. G.f.: x * d/dx Sum_{n=-oo..+oo, n<>0} (1/n^2) * x^(n^2)/(1 - x^n)^n. - Paul D. Hanna, Nov 16 2017 EXAMPLE G.f.: A(x) = 2*x + x^2 + 4*x^3 + 5*x^4 + 6*x^5 + 6*x^6 + 8*x^7 + 16*x^8 + 12*x^9 + 15*x^10 + 12*x^11 + 32*x^12 + 14*x^13 + 28*x^14 +... where A(x) = N(x) + P(x) such that N(x) = x*(x-1)^0 + x^2*(x^2-1) + x^3*(x^3-1)^2 + x^4*(x^4-1)^3 + x^5*(x^5-1)^4 + x^6*(x^6-1)^5 + x^7*(x^7-1)^6 + x^8*(x^8-1)^7 +... P(x) = x/(1-x)^2 + x^4/(1-x^2)^3 + x^9/(1-x^3)^4 + x^16/(1-x^4)^5 + x^25/(1-x^5)^6 + x^36/(1-x^6)^7 + x^49/(1-x^7)^8 +... explicitly, N(x) = x - x^2 + x^3 + x^5 - 3*x^6 + x^7 + 2*x^8 + 2*x^9 - 5*x^10 + x^11 + x^12 + x^13 - 7*x^14 + 7*x^15 + 7*x^16 + x^17 - 19*x^18 + x^19 + 4*x^20 +... P(x) = x + 2*x^2 + 3*x^3 + 5*x^4 + 5*x^5 + 9*x^6 + 7*x^7 + 14*x^8 + 10*x^9 + 20*x^10 + 11*x^11 + 31*x^12 + 13*x^13 + 35*x^14 + 25*x^15 +... PROG (PARI) {a(n) = polcoeff(sum(m=-n-1, n+1, if(m!=0, x^(m^2)/(1-x^m +x*O(x^n))^(m+1))), n)} for(n=1, 60, print1(a(n), ", ")) (PARI) {a(n) = polcoeff(sum(m=-n-1, n+1, if(m!=0, x^m*(x^m-1 +x*O(x^n))^(m-1))), n)} for(n=1, 60, print1(a(n), ", ")) (PARI) {a(n) = polcoeff(sum(m=-n-1, n+1, x^(m^2)/(1+x^m +x*O(x^n))^m), n)} for(n=1, 60, print1(a(n), ", ")) (PARI) {a(n) = polcoeff(sum(m=-n-1, n+1, (1 + x^m +x*O(x^n))^m), n)} for(n=1, 60, print1(a(n), ", ")) CROSSREFS Cf. A261605. Sequence in context: A326058 A262586 A058359 * A110332 A052947 A159287 Adjacent sequences:  A261605 A261606 A261607 * A261609 A261610 A261611 KEYWORD nonn AUTHOR Paul D. Hanna, Aug 26 2015 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 December 14 17:44 EST 2019. Contains 329979 sequences. (Running on oeis4.)