A372520 G.f. A(x) satisfies A(A(A(A(A(x))))) = Sum_{k>=1} k * 25^(k-1) * x^k.

0, 1, 10, -25, 1000, -18125, 131250, 11609375, -630156250, 4314062500, 1173535156250, -38006699218750, -4262573730468750, 321379049072265625, 20787043081054687500, -3209395283374023437500, -116229452332824707031250, 39638105812041778564453125

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

Define the sequence b(n,m) as follows. If n<m, b(n,m) = 0, else if n=m, b(n,m) = 1, otherwise b(n,m) = 1/5 * ( 25^(n-m) * binomial(n+m-1,2*m-1) - Sum_{l=m+1..n-1} (b(n,l) + Sum_{k=l..n} (b(n,k) + Sum_{j=k..n} (b(n,j) + Sum_{i=j..n} b(n,i) * b(i,j)) * b(j,k)) * b(k,l)) * b(l,m) ). a(n) = b(n,1).

Crossrefs

Cf. A309509, A372492, A372499, A372522.

Cf. A141120.

Sequence in context: A156183 A124870 A078257 * A059198 A259297 A358774

Adjacent sequences: A372517 A372518 A372519 * A372521 A372522 A372523

Keyword

sign

Author

Seiichi Manyama, May 04 2024

Status

approved