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Search: id:A041001
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| A041001 |
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Convolution of A000108(n+1), n >= 0, (Catalan numbers) with A038845 (3-fold convolution of powers of 4). |
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+0
3
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| 1, 14, 125, 906, 5810, 34364, 191901, 1026610, 5312230, 26767940, 131990066, 639210404, 3048892740, 14354652152, 66828135005, 308078809794, 1408022619806, 6385966846580, 28765327498278, 128777533131500
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Also convolution of A038836 with A000984 (central binomial coefficients); also convolution of A001791(n+1), n >= 0, with A002802; also convolution of A008549(n+1), n >= 0, with A002697; also convolution of A029760 with A002457; also convolution of A038806(n+1), n >= 0, with A000302 (powers of 4).
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FORMULA
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a(n) = (n+3)*(3*(n+6)*2^(2*n+3)-(n+4)*binomial(2*n+7, n+3))/12; G.f. (c(x)^2)/(1-4*x)^3, where c(x) = g.f. for Catalan numbers.
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CROSSREFS
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Sequence in context: A167602 A155637 A126535 this_sequence A025211 A026870 A090296
Adjacent sequences: A040998 A040999 A041000 this_sequence A041002 A041003 A041004
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KEYWORD
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easy,nonn
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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