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A279284
Self-composition of the pentagonal numbers; g.f.: A(x) = G(G(x)), where G(x) = g.f. of A000326.
0
0, 1, 10, 74, 469, 2662, 14115, 71360, 348143, 1652200, 7669883, 34969286, 157060011, 696514465, 3055404733, 13277356490, 57222978070, 244831062184, 1040760406476, 4398642943496, 18493603597214, 77388169532299, 322451025667910, 1338291853544522, 5534486308363461, 22812231761335189, 93741611639348947, 384122032722040412
OFFSET
0,3
LINKS
FORMULA
G.f.: x*(1 - x)^3*(1 + 2*x)*(1 - x + 7*x^2 - x^3)/(1 - 4*x + x^2 - x^3)^3.
a(n) = 12*a(n-1) - 51*a(n-2) + 91*a(n-3) - 75*a(n-4) + 66*a(n-5) - 28*a(n-6) + 15*a(n-7) - 3*a(n-8) + a(n-9).
MATHEMATICA
CoefficientList[Series[x (1 - x)^3 (1 + 2 x) (1 - x + 7 x^2 - x^3)/(1 - 4 x + x^2 - x^3)^3, {x, 0, 25}], x]
LinearRecurrence[{12, -51, 91, -75, 66, -28, 15, -3, 1}, {0, 1, 10, 74, 469, 2662, 14115, 71360, 348143}, 26]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Dec 09 2016
STATUS
approved