

A055375


Euler transform of Pascal's triangle A007318.


0



1, 1, 1, 2, 3, 2, 3, 7, 7, 3, 5, 14, 21, 14, 5, 7, 26, 48, 48, 26, 7, 11, 45, 103, 131, 103, 45, 11, 15, 75, 198, 312, 312, 198, 75, 15, 22, 120, 366, 674, 830, 674, 366, 120, 22, 30, 187, 637, 1359, 1961, 1961, 1359, 637, 187, 30, 42, 284, 1078, 2584, 4302, 5066
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OFFSET

0,4


COMMENTS

Number of partitions of n objects, k of which are black, into parts each of which is a sequence of objects. E.g. T(3,1) = 7; the partitions are [BWW], [WBW], [WWB], [BW,W], [WB,W], [WW,B] and [B,W,W].  Franklin T. AdamsWatters, Jan 10 2007


LINKS

Table of n, a(n) for n=0..60.
N. J. A. Sloane, Transforms
Index entries for triangles and arrays related to Pascal's triangle


FORMULA

G.f. = Product_{i=1}^{infinity} Product_{j=0}^i 1/(1  x^i y^j)^C(i,j).  Franklin T. AdamsWatters, Jan 10 2007


EXAMPLE

1; 1,1; 2,3,2; 3,7,7,3; 5,14,21,14,5; ...


MATHEMATICA

nmax = 10; pp = Product[Product[1/(1  x^i*y^j)^Binomial[i, j], {j, 0, i}], {i, 1, nmax}]; t[n_, k_] := SeriesCoefficient[pp, {x, 0, n}, {y, 0, k}]; Table[t[n, k], {n, 0, nmax}, {k, 0, n}] // Flatten (* JeanFrançois Alcover, Jul 18 2017 *)


CROSSREFS

Row sums give A034899.
Sequence in context: A264506 A085204 A228527 * A091533 A055376 A085215
Adjacent sequences: A055372 A055373 A055374 * A055376 A055377 A055378


KEYWORD

nonn,tabl


AUTHOR

Christian G. Bower, May 16 2000


STATUS

approved



