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

1,2

Comments

Shape sequence for A122454 is A000041 which counts numeric partitions.

Links

Table of n, a(n) for n=1..56.

Formula

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

Example

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;

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

Crossrefs

Cf. A122455.

Sequence in context: A086606 A076112 A208744 * A189650 A083782 A076240

Adjacent sequences: A122451 A122452 A122453 * A122455 A122456 A122457

Keyword

easy,nonn,tabf

Author

Alford Arnold, Sep 18 2006

Extensions

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

Status

approved