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

0,2

Links

Table of n, a(n) for n=0..16.

Index entries for linear recurrences with constant coefficients, signature (84,-1974,12916,-11025).

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).

Prog

(PARI) a(n) = (49^(n+3)-5*25^(n+3)+9^(n+4)-5)/46080;
(PARI) my(N=20, x='x+O('x^N)); Vec(1/((1-x)*(1-9*x)*(1-25*x)*(1-49*x)))

Crossrefs

Column k=7 of A381512.

Sequence in context: A075909 A132052 A273438 * A097840 A224177 A223869

Adjacent sequences: A381510 A381511 A381512 * A381514 A381515 A381516

Keyword

nonn,easy

Author

Seiichi Manyama, May 11 2025

Status

approved