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A262227 Eulerian numbers of type D, the complementary type. 1
0, 0, 1, 0, 4, 0, 0, 13, 10, 1, 0, 40, 112, 40, 0, 0, 121, 836, 846, 116, 1, 0, 364, 5264, 11784, 5264, 364, 0, 0, 1093, 30318, 129879, 129844, 30339, 1086, 1, 0, 3280, 165792, 1242672, 2337472, 1242672, 165792, 3280, 0, 0, 9841, 878152, 10854028, 34706584, 34706710, 10853944, 878188, 9832, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Named D~(n, k) (the complementary type D triangle) in the Borowiec link.

LINKS

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

Anna Borowiec, Wojciech Mlotkowski, New Eulerian numbers of type D, arXiv:1509.03758 [math.CO], 2015.

FORMULA

T(n, k) = (A060187(n+1, k+1) - (-1)^k*binomial(n, k))/2.

EXAMPLE

Triangle begins:

0;

0, 1;

0, 4, 0;

0, 13, 10, 1;

0, 40, 112, 40, 0;

0, 121, 836, 846, 116, 1;

0, 364, 5264, 11784, 5264, 364, 0;

...

PROG

(PARI) B(n, k) = if( n<k || k<1, 0, sum(i=1, k, (-1)^(k-i) * binomial(n, k-i) * (2*i-1)^(n-1)));

T(n, k) = (A060187(n+1, k+1) - (-1)^k*binomial(n, k))/2;

CROSSREFS

Cf. A060187, A262226.

Sequence in context: A178517 A049207 A092219 * A069026 A133851 A062685

Adjacent sequences:  A262224 A262225 A262226 * A262228 A262229 A262230

KEYWORD

nonn,tabl

AUTHOR

Michel Marcus, Sep 15 2015

STATUS

approved

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Last modified November 18 21:51 EST 2017. Contains 294912 sequences.