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 A107967 a(n) = (n+1)(n+2)^3*(n+3)^2*(n+4)(n^2 + 4n + 5)/1440. 1
 1, 30, 340, 2275, 10878, 41160, 131040, 365310, 916575, 2110966, 4528524, 9150505, 17568460, 32272800, 57041664, 97454268, 161556525, 260710590, 410664100, 632879247, 956166442, 1418672200, 2070276000, 2975456250, 4216691115 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Kekulé numbers for certain benzenoids. LINKS Colin Barker, Table of n, a(n) for n = 0..1000 S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 230). Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1). FORMULA From Colin Barker, Apr 22 2020: (Start) G.f.: (1 + 20*x + 85*x^2 + 105*x^3 + 38*x^4 + 3*x^5) / (1 - x)^10. a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>9. (End) MAPLE a:=n->(1/1440)*(n+1)*(n+2)^3*(n+3)^2*(n+4)*(n^2+4*n+5): seq(a(n), n=0..30); PROG (PARI) Vec((1 + 20*x + 85*x^2 + 105*x^3 + 38*x^4 + 3*x^5) / (1 - x)^10 + O(x^30)) \\ Colin Barker, Apr 22 2020 CROSSREFS Sequence in context: A227689 A006859 A341557 * A115500 A214085 A125418 Adjacent sequences:  A107964 A107965 A107966 * A107968 A107969 A107970 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Jun 12 2005 STATUS approved

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Last modified December 7 20:40 EST 2021. Contains 349589 sequences. (Running on oeis4.)