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 A199746 E.g.f.: 1/(1 + Sum_{n>=1} (-1)^n*x^(n*(3*n-1)/2)/(n*(3*n-1)/2)! + (-1)^n*x^(n*(3*n+1)/2)/(n*(3*n+1)/2)! ). 0
 1, 1, 3, 12, 66, 449, 3678, 35111, 383192, 4704300, 64172052, 962908056, 15762088585, 279514500434, 5338014558032, 109224066408835, 2383887010044728, 55281768382909480, 1357381019671809552, 35180557115610914376, 959798458208463538416, 27494554196938752676656 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA a(n) is odd iff n is a generalized pentagonal number (A001318). EXAMPLE E.g.f.: A(x) = 1 + x + 3*x^2/2! + 12*x^3/3! + 66*x^4/4! + 449*x^5/5! + 3678*x^6/6! +... where the reciprocal involves generalized pentagonal factorials: A(x) = 1/(1 - x - x^2/2! + x^5/5! + x^7/7! - x^12/12! - x^15/15! + x^22/22! + x^26/26! - x^35/35! - x^40/40! +...). PROG (PARI) {a(n)=n!*polcoeff(1/(1+sum(m=1, n, (-1)^m*x^(m*(3*m-1)/2)/(m*(3*m-1)/2)!+(-1)^m*x^(m*(3*m+1)/2)/(m*(3*m+1)/2)! +x*O(x^n))), n)} CROSSREFS Cf. A001318. Sequence in context: A214565 A267323 A058790 * A293302 A248871 A080599 Adjacent sequences: A199743 A199744 A199745 * A199747 A199748 A199749 KEYWORD nonn AUTHOR Paul D. Hanna, Nov 09 2011 STATUS approved

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Last modified February 4 19:33 EST 2023. Contains 360059 sequences. (Running on oeis4.)