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 A326603 E.g.f.: Sum_{n>=0} (x^(2*n-1) + 1)^n * x^n * exp(-x^(2*n+1)) / n!, an even function. 2
 1, 4, -22, 2, 60482, -4838398, 119750402, 7264857602, -348713164798, 4268249137152002, -2020660279013375998, 327387513566969856002, -17234677825923317759998, 20004536762232422400002, 12702000644400049997414400002, -4420880996869850977271807999998, 55184528880536814259678111334400002, -98410947805609541237532965260492799998, 61998887798316869577999908025139200000002 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Paul D. Hanna, Table of n, a(n) for n = 0..260 FORMULA G.f. A(x) = Sum_{n>=0} a(n)*x^(2*n)/(2*n)!, where (1) A(x) = Sum_{n>=0} (x^(2*n-1) + 1)^n * x^n * exp(-x^(2*n+1)) / n!, (2) A(x) = Sum_{n>=0} (x^(2*n-1) - 1)^n * x^n * exp(+x^(2*n+1)) / n!. EXAMPLE E.g.f.: A(x) = 1 + 4*x^2/2! - 22*x^4/4! + 2*x^6/6! + 60482*x^8/8! - 4838398*x^10/10! + 119750402*x^12/12! + 7264857602*x^14/14! - 348713164798*x^16/16! + 4268249137152002*x^18/18! + ... such that A(x) = exp(-x) + (1 + x)*x*exp(-x^3) + (1 + x^3)^2*x^2*exp(-x^5)/2! + (1 + x^5)^3*x^3*exp(-x^7)/3! + (1 + x^7)^4*x^4*exp(-x^9)/4! + (1 + x^9)^5*x^5*exp(-x^11)/5! + (1 + x^11)^6*x^6*exp(-x^13)/6! + ... also A(x) = exp(+x) - (1 - x)*x*exp(+x^3) + (1 - x^3)^2*x^2*exp(+x^5)/2! - (1 - x^5)^3*x^3*exp(+x^7)/3! + (1 - x^7)^4*x^4*exp(+x^9)/4! - (1 - x^9)^5*x^5*exp(+x^11)/5! + (1 - x^11)^6*x^6*exp(+x^13)/6! + ... PROG (PARI) {a(n) = my(A = sum(m=0, 2*n+1, (x^(2*m-1) + 1 +O(x^(2*n+2)) )^m * x^m * exp(-x^(2*m+1) +O(x^(2*n+2))) / m! )); (2*n)!*polcoeff(A, 2*n)} for(n=0, 30, print1(a(n), ", ")) (PARI) {a(n) = my(A = sum(m=0, 2*n+1, (x^(2*m-1) - 1 +O(x^(2*n+2)) )^m * x^m * exp(+x^(2*m+1) +O(x^(2*n+2))) / m! )); (2*n)!*polcoeff(A, 2*n)} for(n=0, 30, print1(a(n), ", ")) CROSSREFS Cf. A326602. Sequence in context: A000868 A000875 A094046 * A335697 A121006 A268924 Adjacent sequences: A326600 A326601 A326602 * A326604 A326605 A326606 KEYWORD sign AUTHOR Paul D. Hanna, Aug 08 2019 STATUS approved

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Last modified September 21 02:47 EDT 2023. Contains 365486 sequences. (Running on oeis4.)