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A262226 Eulerian numbers of type D, the primary type. 1
1, 1, 0, 1, 2, 1, 1, 10, 13, 0, 1, 36, 118, 36, 1, 1, 116, 846, 836, 121, 0, 1, 358, 5279, 11764, 5279, 358, 1, 1, 1086, 30339, 129844, 129879, 30318, 1093, 0, 1, 3272, 165820, 1242616, 2337542, 1242616, 165820, 3272, 1, 1, 9832, 878188, 10853944, 34706710, 34706584, 10854028, 878152, 9841, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Named D(n, k) (the primary type D triangle) in 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:

1;

1, 0;

1, 2, 1;

1, 10, 13, 0;

1, 36, 118, 36, 1;

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

1, 358, 5279, 11764, 5279, 358, 1;

...

MATHEMATICA

T[n_, k_] := (Sum[(-1)^(k-i+1)(2i-1)^n Binomial[n+1, k-i+1], {i, 1, k+1}] + (-1)^k Binomial[n, k])/2;

Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* Jean-Fran├žois Alcover, Sep 24 2018 *)

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, A262227.

Sequence in context: A104251 A320576 A153731 * A298158 A154989 A064307

Adjacent sequences:  A262223 A262224 A262225 * A262227 A262228 A262229

KEYWORD

nonn,tabl

AUTHOR

Michel Marcus, Sep 15 2015

STATUS

approved

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Last modified December 14 04:53 EST 2018. Contains 318090 sequences. (Running on oeis4.)