A381513 Expansion of 1/((1-x) * (1-9*x) * (1-25*x) * (1-49*x)).
1, 84, 5082, 273988, 14057043, 704652312, 34924991284, 1721255653656, 84589852475205, 4151111343284620, 203559674043568206, 9978304519004079804, 489033934020664081687, 23965088084608743341808, 1174349949111469898739048, 57544663330834689436581232, 2819726398822301040064135689
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (84,-1974,12916,-11025).
Crossrefs
Column k=7 of A381512.
Programs
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PARI
a(n) = (49^(n+3)-5*25^(n+3)+9^(n+4)-5)/46080;
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PARI
my(N=20, x='x+O('x^N)); Vec(1/((1-x)*(1-9*x)*(1-25*x)*(1-49*x)))
Formula
E.g.f.: sinh(x)^7/7! = Sum_{k>=0} a(k) * x^(2*k+7)/(2*k+7)!.
a(n) = (49^(n+3) - 5*25^(n+3) + 9^(n+4) - 5)/46080.
a(n) = 84*a(n-1) - 1974*a(n-2) + 12916*a(n-3) - 11025*a(n-4).
a(n) = (1/645120) * Sum_{k=0..7} (-1)^k * (7-2*k)^(2*n+7) * binomial(7,k).