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 A225121 Number of standard Young tableaux with shapes corresponding to partitions into distinct parts with minimal difference 2. 2
 1, 1, 1, 1, 4, 5, 15, 21, 56, 246, 525, 1573, 5764, 14092, 41405, 136995, 772552, 2148290, 8806629, 31679365, 155743665, 495240074, 2049655762, 7403470138, 32627363920, 207316068370, 784695179515, 3721285661481, 16967347935561, 82192321793926, 455572563875425 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..120 Wikipedia, Young tableau 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) local s; s:=ceil(i*(i+2)/4);       `if`(n=s, h([l[], seq(i-2*j, j=0..iquo(i-1, 2))]), `if`(n>s, 0,        g(n, i-1, l)+`if`(i>n, 0, g(n-i, i-2, [l[], i]))))     end: a:= n-> g(n, n, []): seq(a(n), n=0..35);  # Alois P. Heinz, Apr 29 2013 MATHEMATICA h[l_List] := Module[{n}, n = Length[l]; Total[l]!/Product[Product[1 + l[[i]] - j + Sum[If[l[[k]] >= j, 1, 0], {k, i+1, n}], {j, 1, l[[i]]}], {i, 1, n}]]; g[n_, i_, l_List] := Module[{s}, s = Ceiling[i*(i+2)/4]; If[n==s, h[Join[l, Table[i-2*j, {j, 0, Quotient[i-1, 2]}]]], If[n>s, 0, g[n, i-1, l] + If[i>n, 0, g[n-i, i-2, Append[l, i]]]]]]; a[n_] := g[n, n, {}]; Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Jul 02 2015, after  Alois P. Heinz *) CROSSREFS Cf. A218293 (tableaux with shapes corresponding to partitions into distinct parts). Cf. A000085 (standard Young tableaux for all shapes). Sequence in context: A100234 A007390 A037955 * A267991 A225536 A084179 Adjacent sequences:  A225118 A225119 A225120 * A225122 A225123 A225124 KEYWORD nonn AUTHOR Joerg Arndt, Apr 29 2013 STATUS approved

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Last modified November 18 18:46 EST 2017. Contains 294894 sequences.