A306033
Number of length-n restricted growth strings (RGS) with growth <= nine and first element in [9].
Original entry on oeis.org
1, 9, 126, 2229, 46791, 1126032, 30377223, 904211997, 29347973748, 1029154793775, 38706399597879, 1551902279238186, 65998768155695109, 2964410257125490269, 140111251278756345054, 6946234487211269640633, 360202406323880296650987, 19488725004898446787394016
Offset: 0
-
b:= proc(n, m) option remember; `if`(n=0, 1,
add(b(n-1, max(m, j)), j=1..m+9))
end:
a:= n-> b(n, 0):
seq(a(n), n=0..25);
# second Maple program:
a:= n-> n!*coeff(series(exp(add((exp(j*x)-1)/j, j=1..9)), x, n+1), x, n):
seq(a(n), n=0..25);
A306034
Number of length-n restricted growth strings (RGS) with growth <= ten and first element in [10].
Original entry on oeis.org
1, 10, 155, 3035, 70500, 1877083, 56019305, 1844512570, 66219313755, 2568394851483, 106837050484924, 4737487302902715, 222819378516865825, 11068264704881204698, 578536038611685742843, 31718762374848254987147, 1818933941414434687198820
Offset: 0
-
b:= proc(n, m) option remember; `if`(n=0, 1,
add(b(n-1, max(m, j)), j=1..m+10))
end:
a:= n-> b(n, 0):
seq(a(n), n=0..25);
# second Maple program:
a:= n-> n!*coeff(series(exp(add((exp(j*x)-1)/j, j=1..10)), x, n+1), x, n):
seq(a(n), n=0..25);
A355427
Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. 1/(1 - Sum_{j=1..k} (exp(j*x) - 1)/j).
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 3, 0, 1, 3, 11, 13, 0, 1, 4, 24, 89, 75, 0, 1, 5, 42, 284, 959, 541, 0, 1, 6, 65, 654, 4476, 12917, 4683, 0, 1, 7, 93, 1255, 13564, 88178, 208781, 47293, 0, 1, 8, 126, 2143, 32275, 351634, 2084564, 3937019, 545835, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, ...
0, 3, 11, 24, 42, 65, ...
0, 13, 89, 284, 654, 1255, ...
0, 75, 959, 4476, 13564, 32275, ...
0, 541, 12917, 88178, 351634, 1037479, ...
A355423
Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. exp(Sum_{j=1..k} (exp(j*x) - 1)).
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 3, 2, 0, 1, 6, 14, 5, 0, 1, 10, 50, 81, 15, 0, 1, 15, 130, 504, 551, 52, 0, 1, 21, 280, 2000, 5870, 4266, 203, 0, 1, 28, 532, 6075, 35054, 76872, 36803, 877, 0, 1, 36, 924, 15435, 148429, 684000, 1111646, 348543, 4140, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, 1, 3, 6, 10, 15, ...
0, 2, 14, 50, 130, 280, ...
0, 5, 81, 504, 2000, 6075, ...
0, 15, 551, 5870, 35054, 148429, ...
0, 52, 4266, 76872, 684000, 4004100, ...