OFFSET
0,2
COMMENTS
A quadrisection of A249787.
FORMULA
E.g.f.: Series_Reversion(x - 4*x^5/5).
E.g.f.: Sum_{n>=0} x^(4*n+1)/(4*n+1)! * Product_{k=0..n-1} 4*(5*k+4)!/(5*k)!.
a(n) = Product_{k=0..n-1} 4*(5*k+4)!/(5*k)!.
a(n) = A249787(4*n+1).
For n>0, a(n) = 4^n * (5*n-1)! / ((n-1)! * 5^(n-1)). - Vaclav Kotesovec, Nov 15 2014
a(n) ~ 2^(2*n) * 5^(4*n+1/2) * n^(4*n) / exp(4*n). - Vaclav Kotesovec, Nov 15 2014
Recurrence: a(n)+(-2500*n^4+5000*n^3-3500*n^2+1000*n-96)*a(n-1) = 0, a(0) = 1. - Georg Fischer, May 29 2021
EXAMPLE
E.g.f.: A(x) = x + 96*x^5/5! + 1161216*x^9/9! + 111588212736*x^13/13! + 41521527606214656*x^17/17! + 42355944224989145726976*x^21/21! +...+ (4/5)^n * (5*n)!/n! * x^(4*n+1)/(4*n+1)! +...
MAPLE
rec:={a(n)+(sum([-96, 1000, -3500, 5000, -2500][i+1]*n^i, i=0..4)*a(n-1))=0, a(0)=1}; f:= gfun:-rectoproc(rec, a(n), remember): map(f, [$0..10]); # Georg Fischer, May 29 2021
MATHEMATICA
Join[{1}, Table[4^n*(5*n-1)!/((n-1)!*5^(n-1)), {n, 1, 10}]] (* Vaclav Kotesovec, Nov 15 2014 *)
PROG
(PARI) {a(n)=local(A, X=x+x^2*O(x^n)); A=serreverse(X - 4*x^5/5); n!*polcoeff(A, n)}
for(n=0, 15, print1(a(4*n+1), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 14 2014
EXTENSIONS
Offset changed from 1 to 0 by Georg Fischer, May 29 2021
STATUS
approved