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A049400 Partial sums of rows of A047884. Young Tableaux by height. 4
1, 1, 2, 1, 3, 4, 1, 6, 9, 10, 1, 10, 21, 25, 26, 1, 20, 51, 70, 75, 76, 1, 35, 127, 196, 225, 231, 232, 1, 70, 323, 588, 715, 756, 763, 764, 1, 126, 835, 1764, 2347, 2556, 2611, 2619, 2620, 1, 252, 2188, 5544, 7990, 9096, 9415, 9486, 9495, 9496, 1, 462, 5798, 17424, 27908, 33231, 35135, 35596 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Alois P. Heinz, Rows n = 1..44, flattened

Index entries for sequences related to Young tableaux.

EXAMPLE

1;

1,  2;

1,  3,   4;

1,  6,   9,  10;

1, 10,  21,  25,  26;

1, 20,  51,  70,  75,  76;

1, 35, 127, 196, 225, 231, 232;

1, 70, 323, 588, 715, 756, 763, 764;

MAPLE

h:= proc(l) local n; n:=nops(l); add(i, i=l)! /mul(mul(1+l[i]-j+

      add(`if`(l[k]>=j, 1, 0), k=i+1..n), j=1..l[i]), i=1..n)

    end:

g:= proc(n, i, l) option remember;

      `if`(n=0, h(l), `if`(i<1, 0, `if`(i=1, h([l[], 1$n]), g(n, i-1, l)+

      `if`(i>n, 0, g(n-i, i, [l[], i])))))

    end:

T:= (n, k)-> g(n, k, []):

seq(seq(T(n, k), k=1..n), n=1..12); # Alois P. Heinz, Apr 16 2012

MATHEMATICA

Accumulate /@ Table[ Plus @@ NumberOfTableaux /@ Reverse /@ Union[ Sort /@ (Compositions[n - m, m] + 1)], {n, 1, 12}, {m, 1, n}] // Flatten (* Jean-Fran├žois Alcover, Jan 29 2013, after Mathematica program for A047884 *)

CROSSREFS

Cf. A000085, A007579, A007578, A007580, A049401.

Sequence in context: A154929 A249042 A262472 * A283524 A106382 A229287

Adjacent sequences:  A049397 A049398 A049399 * A049401 A049402 A049403

KEYWORD

easy,nice,nonn,tabl

AUTHOR

Alford Arnold

STATUS

approved

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Last modified February 24 14:41 EST 2018. Contains 299623 sequences. (Running on oeis4.)