A245917
Number of pairs of endofunctions f, g on [n] satisfying f(g^8(i)) = f(i) for all i in [n].
Original entry on oeis.org
1, 1, 12, 249, 9184, 488745, 35463456, 3212948809, 454190410752, 85278734539281, 19295679317593600, 4754101825771791801, 1391380506872608002048, 467080657604802224657401, 177425478031159409407340544, 72694051770982862424632639625
Offset: 0
-
with(combinat):
b:= proc(n, i) option remember; unapply(`if`(n=0 or i=1, x^n,
expand(add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*
x^(igcd(i, 8)*j)*b(n-i*j, i-1)(x), j=0..n/i))), x)
end:
a:= n-> add(binomial(n-1, j-1)*n^(n-j)*b(j$2)(n), j=0..n):
seq(a(n), n=0..20);
A245918
Number of pairs of endofunctions f, g on [n] satisfying f(g^9(i)) = f(i) for all i in [n].
Original entry on oeis.org
1, 1, 10, 207, 6856, 302345, 17812656, 1384059775, 131612023936, 30607186160529, 9712391319942400, 2685817593368889551, 809491207939940828160, 280106645752842329055193, 99175751774345673351479296, 36958774352800067430488661375, 15213494922728791702295969038336
Offset: 0
-
with(combinat):
b:= proc(n, i) option remember; unapply(`if`(n=0 or i=1, x^n,
expand(add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*
x^(igcd(i, 9)*j)*b(n-i*j, i-1)(x), j=0..n/i))), x)
end:
a:= n-> add(binomial(n-1, j-1)*n^(n-j)*b(j$2)(n), j=0..n):
seq(a(n), n=0..20);
A245919
Number of pairs of endofunctions f, g on [n] satisfying f(g^10(i)) = f(i) for all i in [n].
Original entry on oeis.org
1, 1, 12, 249, 7744, 401625, 30080736, 3034643689, 371205076992, 52680504366801, 12762075858688000, 4097222646625776921, 1485034580150268715008, 546325401769976582587561, 203541885180568005538811904, 89218786842877518275107415625
Offset: 0
-
with(combinat):
b:= proc(n, i) option remember; unapply(`if`(n=0 or i=1, x^n,
expand(add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*
x^(igcd(i, 10)*j)*b(n-i*j, i-1)(x), j=0..n/i))), x)
end:
a:= n-> add(binomial(n-1, j-1)*n^(n-j)*b(j$2)(n), j=0..n):
seq(a(n), n=0..20);