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A172528 Triangular array T(n,k) n,k>=0 is the number of k letter words formed using at most 1a,2b's,3c's,...,n#'s. 0
1, 1, 1, 1, 2, 3, 3, 1, 3, 8, 19, 38, 60, 60, 1, 4, 15, 53, 175, 535, 1490, 3675, 7700, 12600, 12600, 1, 5, 24, 111, 494, 2111, 8634, 33635, 123998, 428820, 1373820, 4003230, 10325700, 22522500, 37837800, 37837800 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

The row lengths are n(n+1)/2 +1 (A000124).

LINKS

Table of n, a(n) for n=0..40.

FORMULA

E.g.f. for row n is Product_m=0...n[Sum_i=0...m[x^i/i! ]].

EXAMPLE

T(3,2) = 8 because there are 8 two letter words that can be formed using the letters a,b,b,c,c,c: {a, b}, {a, c}, {b, a}, {b, b}, {b, c}, {c, a}, {c, b}, {c, c}.

Triangle Begins

1;

1,1;

1,2,3,3;

1,3,8,19,38,60,60;

1,4,15,53,175,535,1490,3675,7700,12600,12600;

MATHEMATICA

Table[CoefficientList[Series[Product[Sum[x^i/i!, {i, 0, n}], {n, 0, m}], {x, 0, (m^2 + m)/2}], x]*Table[n!, {n, 0, (m^2 + m)/2}], {m, 0, 5}] // Grid

CROSSREFS

The last entry in row n is A022915(n).

Sequence in context: A343533 A308734 A279004 * A087074 A136453 A114104

Adjacent sequences:  A172525 A172526 A172527 * A172529 A172530 A172531

KEYWORD

nonn,tabf

AUTHOR

Geoffrey Critzer, Feb 06 2010

STATUS

approved

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Last modified December 3 21:17 EST 2021. Contains 349468 sequences. (Running on oeis4.)