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A188460 Diagonal sums of number triangle A119308. 1
1, 2, 4, 9, 20, 45, 103, 238, 555, 1305, 3090, 7362, 17637, 42460, 102670, 249246, 607256, 1484343, 3639094, 8946260, 22048771, 54467577, 134842844, 334493154, 831296965, 2069573632, 5160747114, 12888640503, 32234749938, 80728619175, 202433907465 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Hankel transform is  period 12, repeat (1, 0, -1, -2, -1, 0, 1, 1, 0, 0, 0, 1).

LINKS

Table of n, a(n) for n=0..30.

FORMULA

a(n)=sum{k=0..floor(n/2), sum{j=0..n-k, C(n-k,j)*if(k<=j, C(j+1,2*(j-k))*A000108(j-k),0)}}.

G.f.: (1-2*x-x^3-(1-x)*sqrt((x^2-3*x+1)*(x^2+x+1)))/(2*x^5). - Mark van Hoeij, May 10 2013

Conjecture: (n+5)*(n+1)*a(n) -(2*n+5)*(n+2)*a(n-1) -(n+2)*(n+1)*a(n-2) -(n+1)*(2*n+1)*a(n-3) +(n-2)*(n+2)*a(n-4)=0. - R. J. Mathar, Feb 13 2015

PROG

(PARI) x='x+O('x^66); Vec((1-2*x-x^3-(1-x)*sqrt((x^2-3*x+1)*(x^2+x+1)))/(2*x^5)) \\ Joerg Arndt, May 11 2013

CROSSREFS

Sequence in context: A167750 A329276 A308435 * A111099 A000632 A090245

Adjacent sequences:  A188457 A188458 A188459 * A188461 A188462 A188463

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Apr 01 2011

STATUS

approved

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Last modified November 19 22:34 EST 2019. Contains 329323 sequences. (Running on oeis4.)