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%I #17 Jul 03 2023 08:05:48
%S 0,15,2926,567645,110120220,21362755051,4144264359690,803965923024825,
%T 155965244802456376,30256453525753512135,5869596018751378897830,
%U 1138671371184241752666901,220896376413724148638480980
%N Numbers that are both triangular and pentagonal of the second kind.
%D L. E. Dickson, History of the Theory of Numbers. Carnegie Institute Public. 256, Washington, DC, Vol. 1, 1919; Vol. 2, 1920; Vol. 3, 1923, see vol. 2, p. 22.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (195, -195, 1).
%F a(n) = 194 * a(n-1) - a(n-2) + 16.
%F G.f.: x^2 *(15 + x) / ((1 - x) * (1 - 194*x + x^2)).
%F a(n) = A076139(2*n - 2) = A014979(2 - n).
%e 15*x^2 + 2926*x^3 + 567645*x^4 + 110120220*x^5 + 21362755051*x^6 + ...
%e a(4) = 567645 which is 1065*(1065-1)/2 = 615*(3*615+1)/2.
%o (PARI) {a(n) = polchebyshev( 2*n - 2, 2, 7) / 14 + polchebyshev( 2*n - 2, 1, 7) / 84 - 1 / 12} /* _Michael Somos_, Jun 16 2011 */
%Y Cf. A076139, A014979.
%K nonn
%O 1,2
%A _Michael Somos_, May 30 2005
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