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A154029
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List of pairs of numbers:{n^2-1,(2*n-1)!!} such that F((2*n-1)!!)=n^2-1.
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0
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0, 1, 3, 3, 8, 15, 15, 105, 24, 945, 35, 10395, 48, 135135, 63, 2027025, 80, 34459425, 99, 654729075, 120, 13749310575, 143, 316234143225, 168, 7905853580625, 195, 213458046676875, 224, 6190283353629375, 255, 191898783962510625, 288
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| If you have two recursions ( addition and multiplication):
a(0)=-1;a(n)=2*n-1+a(n-1);a(n)=n*(n+1)/2;
and
b(0)=1;b(n)=(2*n-1)*a(n-1):a(n)=n!;
then you can form a function F such that:
F((2*n-1)!!)=n^2-1.
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FORMULA
| {n^2 - 1, (2*n - 1)!!}
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MATHEMATICA
| Clear[a, b, n];
Flatten[Table[{n^2 - 1, (2*n - 1)!!}, {n, 1, 20}]]
(*addition*)
a[0] = -1; a[n_] := a[n] = (2*n - 1) + a[n - 1];
Table[a[n] - (n^2 - 1), {n, 0, 20}]
(*multiplication*)
b[0] = 1; b[n_] := b[n] = (2*n - 1)*b[n - 1];
Table[b[n] - (2*n - 1)!!, {n, 0, 20}]
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CROSSREFS
| Sequence in context: A126073 A126592 A055057 * A104864 A059197 A049974
Adjacent sequences: A154026 A154027 A154028 * A154030 A154031 A154032
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KEYWORD
| nonn,tabf
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 04 2009
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