A352010 -id:A352010 - cp's OEIS frontend

A352009 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-2)^k * a(k) * a(n-2*k-1).

1, 1, 1, -1, -3, -1, 5, 23, 29, -33, -139, -217, 13, 943, 1765, -1545, -8963, -11265, 6229, 73671, 126701, -65713, -567611, -793449, 415197, 4231583, 7471669, -4933529, -37928499, -52823313, 28920485, 346647351, 610476733, -316142785, -2913394667, -4922323705

Offset: 0

Ilya Gutkovskiy, Feb 28 2022

sign

Cf. A015097, A101912, A352010, A352011.

a[0] = 1; a[n_] := a[n] = Sum[(-2)^k a[k] a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 35}]
nmax = 35; A[] = 0; Do[A[x] = 1/(1 - x A[-2 x^2]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

G.f. A(x) satisfies: A(x) = 1 / (1 - x * A(-2*x^2)).

A352011 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-4)^k * a(k) * a(n-2*k-1).

Original entry on oeis.org

1, 1, 1, -3, -7, 5, 33, 269, 393, -1451, -4815, -14115, -2791, 171685, 398145, -3887699, -10399319, 6567925, 63031889, 558518141, 853157689, -4400392635, -14954126751, 29904043597, 151457170889, 344861133205, 170895616881, -12627954103779, -30049168949927

Offset: 0

Ilya Gutkovskiy, Feb 28 2022

sign

Cf. A015099, A101912, A352009, A352010.

a[0] = 1; a[n_] := a[n] = Sum[(-4)^k a[k] a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 28}]
nmax = 28; A[] = 0; Do[A[x] = 1/(1 - x A[-4 x^2]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

G.f. A(x) satisfies: A(x) = 1 / (1 - x * A(-4*x^2)).

cp's OEIS Frontend

A352009 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-2)^k * a(k) * a(n-2*k-1).

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