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A306753
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a(n) = Sum_{k=0..n} binomial(k, 9*(n-k)).
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2
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 11, 56, 221, 716, 2003, 5006, 11441, 24311, 48621, 92380, 167980, 294121, 498751, 824506, 1341154, 2177572, 3605251, 6249101, 11593726, 23138117, 48904469, 106653707, 234305936, 510034166, 1089810953, 2275676459, 4637090547
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OFFSET
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0,11
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = 0..3506
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1,1).
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FORMULA
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G.f.: (1-x)^8/((1-x)^9 - x^10).
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) + a(n-10) for n > 9.
a(n) = A017877(9*n).
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PROG
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(PARI) {a(n) = sum(k=0, n, binomial(k, 9*(n-k)))}
(PARI) N=66; x='x+O('x^N); Vec((1-x)^8/((1-x)^9-x^10))
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CROSSREFS
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Column 9 of A306680.
Cf. A017877.
Sequence in context: A037731 A221019 A115205 * A306860 A212388 A198769
Adjacent sequences: A306750 A306751 A306752 * A306754 A306755 A306756
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KEYWORD
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nonn
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AUTHOR
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Seiichi Manyama, Mar 07 2019
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STATUS
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approved
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