A381513 - OEIS

%I #22 May 12 2025 08:28:04

%S 1,84,5082,273988,14057043,704652312,34924991284,1721255653656,

%T 84589852475205,4151111343284620,203559674043568206,

%U 9978304519004079804,489033934020664081687,23965088084608743341808,1174349949111469898739048,57544663330834689436581232,2819726398822301040064135689

%N Expansion of 1/((1-x) * (1-9*x) * (1-25*x) * (1-49*x)).

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (84,-1974,12916,-11025).

%F E.g.f.: sinh(x)^7/7! = Sum_{k>=0} a(k) * x^(2*k+7)/(2*k+7)!.

%F a(n) = (49^(n+3) - 5*25^(n+3) + 9^(n+4) - 5)/46080.

%F a(n) = 84*a(n-1) - 1974*a(n-2) + 12916*a(n-3) - 11025*a(n-4).

%F a(n) = (1/645120) * Sum_{k=0..7} (-1)^k * (7-2*k)^(2*n+7) * binomial(7,k).

%o (PARI) a(n) = (49^(n+3)-5*25^(n+3)+9^(n+4)-5)/46080;

%o (PARI) my(N=20, x='x+O('x^N)); Vec(1/((1-x)*(1-9*x)*(1-25*x)*(1-49*x)))

%Y Column k=7 of A381512.

%K nonn,easy

%O 0,2

%A _Seiichi Manyama_, May 11 2025