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A229111 Expansion of the g.f. of A053723 in powers of the g.f. of A121591. 0
1, -5, 35, -275, 2275, -19255, 163925, -1385725, 11483875, -91781375, 688658785, -4581861025, 22550427925, 8852899375, -2431720493125, 47471706909725, -699843878180125, 9141002535744625, -111232778205154375, 1288777160650004375, -14372445132730778975 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

In Verrill (1999) section 2.1, t = (eta(q^5) / eta(q))^6 the g.f. of A121591 and f = eta(q^5)^5 / eta(q) the g.f. of A053723.

REFERENCES

H. Verrill, Some Congruences related to modular forms, Max Planck Institute, 1999.

LINKS

Table of n, a(n) for n=1..21.

H. Verrill, Some Congruences related to modular forms

FORMULA

n^3 * a(n+1) = -(2*n - 1)*(11*n*(n - 1) + 5) * a(n) - 125 * (n - 1)^3 * a(n-1).

a(n*p^k) == (p^3 + kronecker(p, 5)) * a(n*p^(k-1)) - kronecker(p, 5) * p^3*a(n*p^(-2)) (mod p^k) [Verrill, 1999]

EXAMPLE

G.f. = x - 5*x^2 + 35*x^3 - 275*x^4 + 2275*x^5 - 19255*x^6 + 163925*x^7 + ...

PROG

(PARI) {a(n) = local(m = n-1); if( n<1, 0, if( n<3, [1, -5][n], -( (5*(m - 1))^3*a(n-2) + (2*m - 1)*(11*(m^2 - m) +5)*a(n-1) )/ m^3))}

CROSSREFS

Cf. A053723, A109064, A121591.

Sequence in context: A180900 A087630 A084135 * A138233 A248053 A002294

Adjacent sequences:  A229108 A229109 A229110 * A229112 A229113 A229114

KEYWORD

sign

AUTHOR

Michael Somos, Sep 30 2013

STATUS

approved

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Last modified March 27 02:57 EDT 2015. Contains 255920 sequences.