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A367414
Expansion of (1/x) * Series_Reversion( x * (1-x-x^4/(1-x)^2) ).
3
1, 1, 2, 5, 15, 51, 187, 715, 2800, 11138, 44846, 182476, 749566, 3105575, 12966165, 54505650, 230508612, 980045835, 4186600220, 17960356014, 77343359518, 334217730014, 1448771849516, 6298222363395, 27452466169243, 119949953637406, 525284132440963
OFFSET
0,3
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} binomial(n+k,k) * binomial(2*n-k,n-4*k).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x-x^4/(1-x)^2))/x)
(PARI) a(n) = sum(k=0, n\4, binomial(n+k, k)*binomial(2*n-k, n-4*k))/(n+1);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 26 2024
STATUS
approved