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A194590 a(n) = (-1)^n*(A056040(n+1)*A152271(n)-2^n)/2. 2
0, 0, 1, -2, 7, -14, 38, -76, 187, -374, 874, -1748, 3958, -7916, 17548, -35096, 76627, -153254, 330818, -661636, 1415650, -2831300, 6015316, -12030632, 25413342, -50826684, 106853668, -213707336, 447472972, -894945944, 1867450648, -3734901296, 7770342787 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The binomial transform of a(n) are the complementary Riordan numbers A194589 (see link).

LINKS

Table of n, a(n) for n=0..32.

Peter Luschny, The lost Catalan numbers

FORMULA

a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n,k)*cr(k), where cr(k) are the complementary Riordan numbers A194589.

MAPLE

A056040 := n -> n!/iquo(n, 2)!^2:

A152271 := n -> `if`(n mod 2 = 0, 1, (n+1)/2):

A194590 := n -> (-1)^n*(A056040(n+1)*A152271(n)-2^n)/2:

MATHEMATICA

sf[n_] := n!/Quotient[n, 2]!^2;

a[n_] := (-1)^n (sf[n + 1] * If[EvenQ[n], 1, (n + 1)/2] - 2^n)/2;

Table[a[n], {n, 0, 32}] (* Jean-Fran├žois Alcover, Jun 26 2019 *)

CROSSREFS

Cf. A107373 (has offset 1).

Sequence in context: A191319 A018497 A178748 * A107373 A176662 A018526

Adjacent sequences:  A194587 A194588 A194589 * A194591 A194592 A194593

KEYWORD

sign

AUTHOR

Peter Luschny, Aug 30 2011

STATUS

approved

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Last modified October 17 21:57 EDT 2019. Contains 328134 sequences. (Running on oeis4.)