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A014942 a(n) = (1 + 24^n*(23*n - 1))/529.

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%I A014942 #16 May 21 2025 01:35:19
%S A014942 1,49,1777,57073,1715953,49491697,1387212529,38078983921,
%T A014942 1028756811505,27446832213745,724884022832881,18985057740861169,
%U A014942 493749574409596657,12764586312924606193,328300388160453422833,8406016915457191128817,214387788361524002631409,5448748098049810036109041
%N A014942 a(n) = (1 + 24^n*(23*n - 1))/529.
%H A014942 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (49,-624,576).
%F A014942 a(n) = a(n-1) + n*24^(n-1).
%F A014942 a(n)= 49*a(n-1) - 624*a(n-2) + 576*a(n-3) for n > 3.
%F A014942 G.f.: x/((1-x)*(1-24*x)^2). - _Joerg Arndt_, May 23 2010
%F A014942 From _Elmo R. Oliveira_, May 18 2025: (Start)
%F A014942 E.g.f.: exp(x)*(1 + exp(23*x)*(552*x - 1))/529.
%F A014942 a(n) = 48*a(n-1) - 576*a(n-2) + 1 for n > 2. (End)
%t A014942 a[1] = 1; a[n_Integer] := a[n - 1] + n*24^(n - 1); Table[ a[n], {n, 1, 20}]
%o A014942 (PARI) Vec(-x/((x-1)*(24*x-1)^2) + O(x^19)) \\ _Elmo R. Oliveira_, May 18 2025
%Y A014942 Cf. A014960.
%K A014942 nonn,easy
%O A014942 1,2
%A A014942 _Olivier Gérard_
%E A014942 More terms from _Robert G. Wilson v_, Sep 15 2000
%E A014942 Exchanged Lava formula of Jan 2009 with the definition [_R. J. Mathar_, May 23 2010]