A217327
Number of self-inverse permutations in S_n with longest increasing subsequence of length 7.
Original entry on oeis.org
1, 7, 55, 319, 1904, 10275, 56135, 294386, 1556323, 8086433, 42298721, 219795160, 1149139210, 5999688692, 31506046052, 165664633982, 875886376212, 4643488263933, 24746018418741, 132328997879066, 711142850556217, 3836134976520394, 20791024498584110
Offset: 7
a(7) = 1: 1234567.
a(8) = 7: 12345687, 12345768, 12346578, 12354678, 12435678, 13245678, 21345678.
A218267
Number of standard Young tableaux of n cells and height >= 7.
Original entry on oeis.org
1, 8, 64, 400, 2465, 14092, 80016, 442248, 2442351, 13375366, 73477622, 403703404, 2230591660, 12380801756, 69225756076, 389806286920, 2213844625658, 12681996193252, 73339826141716, 428242854338216, 2526129602115517, 15056977593085444, 90712249806247400
Offset: 7
-
b:= proc(n) b(n):= `if`(n<2, 1, b(n-1) +(n-1)*b(n-2)) end:
g:= proc(n) option remember;
`if`(n<4, [1, 1, 2, 4][n+1], ((20*n^2+184*n+336)*g(n-1)
+4*(n-1)*(10*n^2+58*n+33)*g(n-2) -144*(n-1)*(n-2)*g(n-3)
-144*(n-1)*(n-2)*(n-3)*g(n-4)) / ((n+5)*(n+8)*(n+9)))
end:
a:= n-> b(n) -g(n):
seq(a(n), n=7..30);
A229068
Number of standard Young tableaux of n cells and height <= 12.
Original entry on oeis.org
1, 1, 2, 4, 10, 26, 76, 232, 764, 2620, 9496, 35696, 140152, 568503, 2390466, 10349340, 46204720, 211779200, 997134592, 4808141824, 23745792032, 119848119307, 618058083314, 3251373425356, 17442275104496, 95297400355320, 530067682582320, 2998503402985440
Offset: 0
Cf.
A182172,
A001405 (k=2),
A001006 (k=3),
A005817 (k=4),
A049401 (k=5),
A007579 (k=6),
A007578 (k=7),
A007580 (k=8),
A212915 (k=9),
A212916 (k=10),
A229053 (k=11).
-
RecurrenceTable[{-147456 (-5+n) (-4+n) (-3+n) (-2+n) (-1+n) (12+n) a[-6+n]-110592 (-4+n) (-3+n) (-2+n) (-1+n) (29+2 n) a[-5+n]+256 (-3+n) (-2+n) (-1+n) (121272+32786 n+2343 n^2+49 n^3) a[-4+n]+128 (-2+n) (-1+n) (438597+90321 n+5391 n^2+98 n^3) a[-3+n]-16 (-1+n) (8718630+5347213 n+804616 n^2+49754 n^3+1372 n^4+14 n^5) a[-2+n]-8 (27335490+10162354 n+1206473 n^2+63328 n^3+1533 n^4+14 n^5) a[-1+n]+(11+n) (20+n) (27+n) (32+n) (35+n) (36+n) a[n]==0, a[1]==1, a[2]==2, a[3]==4, a[4]==10, a[5]==26, a[6]==76}, a, {n, 20}]
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