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A179927 Triangle of centered orthotopic numbers 4
1, 1, 2, 1, 3, 2, 1, 5, 5, 2, 1, 9, 13, 7, 2, 1, 17, 35, 25, 9, 2, 1, 33, 97, 91, 41, 11, 2, 1, 65, 275, 337, 189, 61, 13, 2, 1, 129, 793, 1267, 881, 341, 85, 15, 2 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

T(n, k) = [x^k] series[ H(n - k, x) ]

Here H(n,x) = E(n,x)*(1+x)/(1-x)^(n+1) where E(n,x) are the Eulerian polynomials, E(0,x) = 1 and E(n,x) = sum_{k=0^{n-1}} W_{n,k} x^k for n > 0. W_{n,k} as in DLMF Table 26.14.1.

LINKS

Table of n, a(n) for n=0..44.

Peter Luschny, Figurate number - a very short introduction

EXAMPLE

1

1, 2

1, 3, 2

1, 5, 5, 2

1, 9, 13, 7, 2

1, 17, 35, 25, 9, 2

1, 33, 97, 91, 41, 11, 2

MAPLE

E := (n, x) -> `if`(n=0, 1, x*(1-x)*diff(E(n-1, x), x)+E(n-1, x)*(1+(n-1)*x));

H := (n, x) -> E(n, x)*(1+x)/(1-x)^(n+1);

A179927 := (n, k) -> coeff(series(H(n-k, x), x, 18), x, k);

seq(print(seq(A179927(n, k), k=0..n)), n=0..6);

CROSSREFS

Cf. Row sums in A179928, triangle of orthotopic numbers is A009998.

Sequence in context: A038497 A091355 A131245 * A104446 A131345 A134423

Adjacent sequences:  A179924 A179925 A179926 * A179928 A179929 A179930

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Aug 02 2010

STATUS

approved

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Last modified September 22 09:45 EDT 2017. Contains 292337 sequences.