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 A122454 A triangle with shape A000041 defined by sequence A098546 times sequence A036040. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 21 02:47 EDT 2023. Contains 365486 sequences. (Running on oeis4.)