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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
OFFSET
0,2
COMMENTS
Kekulé numbers for certain benzenoids.
LINKS
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 * A354656 A115500 A214085
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 12 2005
STATUS
approved