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A122454 A triangle with shape A000041 defined by sequence A098546 times sequence A036040.

%I A122454 #10 Sep 17 2017 14:45:09
%S A122454 1,2,1,3,9,1,4,24,18,24,1,5,50,100,100,150,50,1,6,90,225,150,300,1200,
%T A122454 300,300,675,90,1,7,147,441,735,735,3675,2450,3675,1225,7350,3675,735,
%U A122454 2205,147,1,8,224,784,1568,980,1568,9408,15680,11760,15680,3920,29400
%N A122454 A triangle with shape A000041 defined by sequence A098546 times sequence A036040.
%C A122454 Shape sequence for A122454 is A000041 which counts numeric partitions.
%F A122454 A122454(n) = A098546(n) times A036040(n).
%e A122454 A098546(n) begins 1 2 1 3 3 1 4 6 6 4 1 ...
%e A122454 A036040(n) begins 1 1 1 1 3 1 1 4 3 6 1 ...
%e A122454 So the triangle begins:
%e A122454 1;
%e A122454 2,   1;
%e A122454 3,   9,   1;
%e A122454 4,  24,  18,  24,   1;
%e A122454 5,  50, 100, 100, 150,   50,    1;
%e A122454 6,  90, 225, 150, 300, 1200,  300,  300,  675,   90,    1;
%e A122454 7, 147, 441, 735, 735, 3675, 2450, 3675, 1225, 7350, 3675, 735, 2205, 147, 1;
%p A122454 sortAbrSteg := proc(L1,L2) local i ; if nops(L1) < nops(L2) then RETURN(true) ; elif nops(L2) < nops(L1) then RETURN(false) ; else for i from 1 to nops(L1) do if op(i,L1) < op(i,L2) then RETURN(false) ; fi ; od ; RETURN(true) ; fi ; end: A098546 := proc(n,k) local prts,m ; prts := combinat[partition](n) ; prts := sort(prts, sortAbrSteg) ; if k <= nops(prts) then m := nops(op(k,prts)) ; binomial(n,m) ; else 0 ; fi ; end: M3 := proc(L) local n,k,an,resul; n := add(i,i=L) ; resul := factorial(n) ; for k from 1 to n do an := add(1-min(abs(j-k),1),j=L) ; resul := resul/ (factorial(k))^an /factorial(an) ; od ; end: A036040 := proc(n,k) local prts,m ; prts := combinat[partition](n) ; prts := sort(prts, sortAbrSteg) ; if k <= nops(prts) then M3(op(k,prts)) ; else 0 ; fi ; end: A122454 := proc(n,k) A098546(n,k)*A036040(n,k) ; end: for n from 1 to 10 do for k from 1 to combinat[numbpart](n) do a:=A122454(n,k) ; printf("%d, ",a) ; od; od ; # _R. J. Mathar_, Jul 17 2007
%Y A122454 Cf. A122455.
%K A122454 easy,nonn,tabf
%O A122454 1,2
%A A122454 _Alford Arnold_, Sep 18 2006
%E A122454 More terms from _R. J. Mathar_, Jul 17 2007