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A277297 Diagonal of triangle A277295; a(n) = A277295(n+2,n). 5
2, 14, 76, 378, 1808, 8484, 39446, 182732, 846248, 3926338, 18276832, 85436832, 401313288, 1894847846, 8994916236, 42931067910, 206002472336, 993664391720, 4817140123620, 23464959242520, 114820471485840, 564248307992850, 2783898831160512, 13786409317705920, 68509284536815640, 341538385855855064, 1707729163812908528 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
G.f. G(x,y) of triangle A277295 satisfies:
(1) G(x,y) = x + G( y*G(x,y) + (1-y)*x, y)^2.
(2) G( x - y*G(x,y)^2, y) = x + (1-y)*G(x,y)^2.
LINKS
FORMULA
a(n) = 2 * A291822(n) for n >= 1. - Paul D. Hanna, Jul 24 2023
PROG
(PARI) {A277295(n, k) = my(A=x); for(i=1, n, A = x + subst(A^2, x, y*A + (1-y)*x +x*O(x^n)) ); polcoeff(polcoeff(A, n, x), k, y)}
for(n=1, 30, print1(A277295(n+2, n-1), ", "))
CROSSREFS
Sequence in context: A197874 A104871 A172060 * A185055 A034573 A278417
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 11 2016
STATUS
approved

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Last modified May 24 01:38 EDT 2024. Contains 372768 sequences. (Running on oeis4.)