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

1, 2, 1, 3, 9, 1, 4, 24, 18, 24, 1, 5, 50, 100, 100, 150, 50, 1, 6, 90, 225, 150, 300, 1200, 300, 300, 675, 90, 1, 7, 147, 441, 735, 735, 3675, 2450, 3675, 1225, 7350, 3675, 735, 2205, 147, 1, 8, 224, 784, 1568, 980, 1568, 9408, 15680, 11760, 15680, 3920, 29400

Offset: 1

Author

Alford Arnold, Sep 18 2006

Keywords

• easy
• nonn
• tabf

Comments

Shape sequence for A122454 is A000041 which counts numeric partitions.

Examples

			A098546(n) begins 1 2 1 3 3 1 4 6 6 4 1 ...
A036040(n) begins 1 1 1 1 3 1 1 4 3 6 1 ...
So the triangle begins:
1;
2,   1;
3,   9,   1;
4,  24,  18,  24,   1;
5,  50, 100, 100, 150,   50,    1;
6,  90, 225, 150, 300, 1200,  300,  300,  675,   90,    1;
7, 147, 441, 735, 735, 3675, 2450, 3675, 1225, 7350, 3675, 735, 2205, 147, 1;
		

Crossrefs

Cf. A122455.

Programs

Maple

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

Formula

A122454(n) = A098546(n) times A036040(n).

Extensions

More terms from R. J. Mathar, Jul 17 2007