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A264436 Triangle read by rows, inverse Bell transform of the complementary Bell numbers (A000587); T(n,k) for n>=0 and 0<=k<=n. 0
1, 0, 1, 0, 1, 1, 0, 3, 3, 1, 0, 14, 15, 6, 1, 0, 89, 100, 45, 10, 1, 0, 716, 834, 405, 105, 15, 1, 0, 6967, 8351, 4284, 1225, 210, 21, 1, 0, 79524, 97596, 52220, 16009, 3080, 378, 28, 1, 0, 1041541, 1303956, 721674, 233268, 48699, 6804, 630, 36, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Table of n, a(n) for n=0..54.

Peter Luschny, The Bell transform

FORMULA

Row sums are A029768(n-1) for n>=1.

T(n,1) = A007549(n) for n>=1.

EXAMPLE

Triangle starts:

1,

0,     1,

0,     1,     1,

0,     3,     3,     1,

0,    14,    15,     6,     1,

0,    89,   100,    45,    10,    1,

0,   716,   834,   405,   105,   15,   1,

0,  6967,  8351,  4284,  1225,  210,  21,  1,

0, 79524, 97596, 52220, 16009, 3080, 378, 28, 1

PROG

(Sage)

# The function bell_transform is defined in A264428.

# The function inverse_bell_transform is defined in A264429.

def A264436_matrix(dim):

    uno = [1]*dim

    complementary_bell_numbers = [sum((-1)^n*b for (n, b) in enumerate (bell_transform(n, uno))) for n in (0..dim)]

    return inverse_bell_transform(dim, complementary_bell_numbers)

A264436_matrix(9)

CROSSREFS

Cf. A000587, A007549, A029768, A264428, A264429.

Sequence in context: A092747 A265608 A184962 * A122850 A132062 A065547

Adjacent sequences:  A264433 A264434 A264435 * A264437 A264438 A264439

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Dec 01 2015

STATUS

approved

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Last modified September 17 06:41 EDT 2019. Contains 327119 sequences. (Running on oeis4.)