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 A360321 a(n) = Sum_{k=0..n} 5^(n-k) * binomial(n-1,n-k) * binomial(2*k,k). 4
 1, 2, 16, 130, 1070, 8902, 74724, 631902, 5376840, 45990070, 395106656, 3407196982, 29477061166, 255733684010, 2224098916300, 19384492018770, 169270624419390, 1480625235653670, 12970844831940000, 113785067475668550, 999400688480388570 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..20. FORMULA G.f.: sqrt( (1-5*x)/(1-9*x) ). n*a(n) = 2*(7*n-6)*a(n-1) - 45*(n-2)*a(n-2). Sum_{i=0..n} Sum_{j=0..i} (1/5)^i * a(j) * a(i-j) = (9/5)^n. a(n) ~ 2 * 3^(2*n-1) / sqrt(Pi*n). - Vaclav Kotesovec, Feb 04 2023 PROG (PARI) a(n) = sum(k=0, n, 5^(n-k)*binomial(n-1, n-k)*binomial(2*k, k)); (PARI) my(N=30, x='x+O('x^N)); Vec(sqrt((1-5*x)/(1-9*x))) CROSSREFS Cf. A063886, A085362, A360317, A360318, A360319, A360322. Sequence in context: A037720 A022018 A067684 * A074623 A323946 A275636 Adjacent sequences: A360318 A360319 A360320 * A360322 A360323 A360324 KEYWORD nonn,easy AUTHOR Seiichi Manyama, Feb 03 2023 STATUS approved

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Last modified November 28 08:03 EST 2023. Contains 367394 sequences. (Running on oeis4.)