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A306280
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a(n) = Sum_{k=0..n} binomial(n,k)*binomial(n^2+k,k).
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1
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1, 3, 26, 416, 9708, 297662, 11306572, 512307336, 26968496504, 1617489748394, 108885682104744, 8129721925098468, 666736347200187804, 59582961423951290184, 5762936296492591067968, 599807329803134064385488, 66843498592187788579795440
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listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = 0..337
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FORMULA
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From Vaclav Kotesovec, Feb 08 2019: (Start)
a(n) ~ exp(1) * A135860(n).
a(n) ~ exp(n + 3/2) * n^(n - 1/2) / sqrt(2*Pi). (End)
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MATHEMATICA
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a[n_] := Sum[Binomial[n, k] * Binomial[n^2+k, k], {k, 0, n}]; Array[a, 20, 0] (* Amiram Eldar, Feb 03 2019 *)
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PROG
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(PARI) {a(n) = sum(k=0, n, binomial(n, k)*binomial(n^2+k, k))}
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CROSSREFS
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Cf. A001850, A114496, A135860, A156886, A156887.
Sequence in context: A326431 A206403 A192554 * A305144 A206402 A300954
Adjacent sequences: A306277 A306278 A306279 * A306281 A306282 A306283
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KEYWORD
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nonn
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AUTHOR
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Seiichi Manyama, Feb 02 2019
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STATUS
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approved
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